In this paper we discuss the convergence rate for Galerkin approximation of the stochastic Allen–Cahn equations driven by space-time white noise on T2. 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 forα ∈(0, 2/9) andδ >0 arbitrarily small.