I cannot positively say that Simon does not believe in the existence of a beast on the island with the boys. What I can say is that Simon's belief in a "beast" is quite different from the beliefs of the other boys. Many of the boys believe that the beast on the island is a big beast with sharp teeth, claws, and so on. They believe it is something that can be hunted down and killed. Simon's beast is more abstract. He believes that the beast is inside each of the boys. The beast is man's ability and desire to act as a savage beast and do harm upon his fellow man. Simon correctly realizes that the boys are a greater risk to each other than any other possible beast that might exist on the island.

However Simon thought of the beast, there rose before his inward sight the picture of a human at once heroic and sick.

If readers need a proof of concept of Simon's theory about the beast, readers need look no further than Jack and Roger.

In chapter 5, Ralph brings up the existence of the beast at the assembly. Ralph begins by saying that there is absolutely no possible way a beast inhabits the island and Jack agrees with his statement. Piggy also agrees that there is no beast on the island and looks at the situation pragmatically. Piggy believes that "life is scientific" and does not think that it is possible for a massive beast to exist on such a small tropical island. However, Simon understands the true nature of the beast but cannot articulate his thoughts during the assembly because of his fear of public speaking. Simon is a symbolic Christ figure throughout the novel and thoroughly understands that the beast is the inherent wickedness present in each boy.

At the beginning of chapter 6, Samneric claim that they witnessed the beast on the top of the mountain. All of the boys, except Simon, believe Samneric's story and form a hunting party to search for the beast. As the boys explore the island looking for the beast, Simon experiences a feeling of disbelief. Golding writes,

However Simon thought of the beast, there rose before his inward sight the picture of a human at once heroic and sick (79).

Simon's unique insight into the true nature of the beast prevents him from believing that there is a malevolent physical creature on the island. Simon is the only boy not scared of the beast because he understands that it is the inherent wickedness of each boy.

I think you mean that Simon is the only one to doubt the existence of the "beast". As the boys walk, Simon thinks about whether the beast does exist. His contemplation of the beast's existence is described. "However Simon thought of the beast, there rose before his inward sight the picture of a human at once heroic and sick." For the other boys, the beast has become an actual form, the corpse on top...