There are plenty of moral lessons that can be drawn from The Old Man and the Sea. Some of the more obvious ones include the following:

Persistence is a virtue: The entire story is based on the old man's refusal to give up in his battle with the fish. His determination, even when he seems overmatched in his little boat, is meant to be admired.

Being true to oneself: The old man is completely secure in his identity as a fisherman and does not measure his self worth in terms of what he catches. His fishing ability is inborn, and his knowledge of the sea is instinctive.

Courage: The old man's battle with the fish is a kind of ultimate test of his courage, although the old man does not think about it in that way. Hemingway's famous definition of courage as "grace under pressure" comes into play here, as the fisherman's courage is less a conscious decision on his part than it is something necessary in order for him to perform his work.

One's work should be one's art: The fisherman's adventure with the fish is a kind of expression of the artist at work, struggling with his material. In another sense, the instinctive way the old man approaches fishing is similar to the way the artist develops his work. In either case, his fishing is an expression of his inner personality and passion.

The end is less important than the means: It is significant that the old man is not able to bring the fish to market and that all that is left of it in the end is the skeleton. What is important about the old man's struggle is not what he acquires, but how his struggle validates his identity as a fisherman.

An important moral lesson in The Old Man and the Sea can be summed up in the maxim "the journey is the reward."

Santiago uses courage, skill, determination, and the wisdom of long experience to catch the giant marlin, which is longer than his boat. Sharks eat all the meat, despite Santiago's best attempts to fight them off. Santiago enters the harbor with nothing to sell, only a huge skeleton. The important point, however, is that Santiago caught the fish. He fought the good fight with every ounce of strength he had and that is the true victory, not how much money he might have made. He has been true to himself and lived with integrity.

A related moral is Santiago's optimistic conviction that “man is not made for defeat. ... A man can be destroyed but not defeated.”

By "man," Santiago means what he believes is a true man: a person who faces his adversaries with all he has and doesn't give in. Santiago might have "lost" to the sharks, but he hasn't really lost because he has, all along, faced them with courage and honor.

Finally, another important moral of the story can be summed up in these lines:

Now is no time to think of what you do not have. Think of what you can do with what there is.

Santiago is an old man. He hasn't caught a fish in a long time, his boat and equipment aren't the best, and he isn't as strong as he once was. However, he lets none of this deter him as he faces his battle with the marlin and the sharks. When his harpoon breaks, he fights off the sharks with a piece of wood. He always makes the best of the resources he has at hand, knowing that success in life comes from relying on one's inner, not outer, strength.

From the book the Old Man and the Sea, several morals are observed. For instance, Santiago demonstrates persistence in his fishing endeavor. Despite going for more than eighty days without a single catch, each evening going home empty-handed, Santiago does not relent and still goes out to fish. Humility is also shown when Santiago accepts Manolin’s kindness. He put aside his pride and accepted assistance from a young boy that pitied him. Manolin portrays loyalty by ensuring that Santiago has enough to eat. He also ensures that Santiago has fresh bait for his lines, going to the extent of stealing or begging to make sure the above needs are met. He does all this despite his father’s advice to stop associating with Santiago. Santiago demonstrates patience by pursuing the marlin overnight, waiting for it to tire. He is resourceful, eating raw tuna. He also consumes water carefully not to exhaust it, aware that he is long way from shore. 

Morality is a funny word here, it seems to me.  It implies the rightness and wrongness of things rather than observations about the character of things. 

Pereseverence in the face of adversity is clearly evident in this novella; however, I'm not so sure that's a moral quality.  Certainly moral people can demonstrate perseverence, but so can immoral people.

The same is probably true for this issue, as well, but it's all I can envision to fit the word moral. I'd have to go to the catching of the fish for any moral perspective from the story.  Santiago is respectful of his environment.  He only takes the bait he needs, and he isn't wasteful--as he only keeps the tuna because he will eat it.  He is respectful of his opponent, his brother, the great fish.  He understands this is a battle, but Santiago does fight like a gentleman and respects his foe. 

Respect for others and one's surroundings (as demonstrated by Manolin's respect for Santiago, as well) is one of the only real "moral" issues I find in this work.