In this paper we discuss the convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations driven by space-time white noise on T 2 . First we prove that the convergence rate for stochastic 2D heat equation is of order α − δ in Besov space C −α for α ∈ (0, 1) and δ > 0 arbitrarily small. Then we obtain the convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations of order α − δ in C −α for α ∈ (0, 2/9) and δ > 0 arbitrarily small.