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We have studied diffusion in a quasi-two-dimensional granular gas composed of plastic balls confined in a vertically vibrating thin box. The horizontal motion of the balls in the box is found to follow the Langevin equation with the top and bottom of the box acting on the balls with a viscous drag like that in a fluid. Surprisingly, we find that both the granular temperature and the diffusion constant increase with the number of balls $(N)$ in the box for small $N$. The unusual diffusion can be explained by a two-state model, in which a ball is in contact with two effective temperature baths due to collisions with the top or bottom of the box and collisions with other balls.