Definitions of anti-hero vary slightly from source to source, but a good working definition is that an anti-hero is a story's protagonist that doesn't adhere to the traditional characteristics of a hero. The anti-hero is generally more flawed than most characters and disturbs readers with those weaknesses. This hero type is generally someone that doesn't fit the trustworthy, courageous, and honest characteristics of a normal hero, yet we can't help but sympathize and root for the character. A good modern film example would be Riddick from the movie Pitch Black and following sequels. To be clear, Grendel, as portrayed in the original poem, is not an anti-hero. He is pure evil. Gardner really throws readers a curve in his retelling of this epic by showing readers that Grendel is not pure evil. For sure, Grendel still murders a lot of people and still eats them, but Grendel is also portrayed as someone with a heart and sense of humor. We are even given gut-wrenching quotes that show Grendel is a character with huge inner turmoil.
Why can't I have someone to talk to?
Gardner even gives readers the idea that Grendel is in a position not by his own choosing. Grendel is the unfortunate side effect of some long lost descendant; therefore, Grendel is living a curse. That curse causes him pain, suffering, isolation, and loneliness.
He told of an ancient feud between two brothers which split all the world between darkness and light. And I, Grendel, was the dark side, he said in effect. The terrible race God cursed.
Deep down, we know that Grendel is doing bad things; however, we also know that he can't always help it. The actions he is taking are still brave. He's stepping into battle with the threat of death. That's a standard hero affair.