In this paper, we investigate the finite fractal dimension of pullback attractors for a nonclassical diffusion equation in $H_0^1(\mathrm{\Omega })$. First, we prove the existence of pullback attractors for a nonclassical diffusion equation with arbitrary polynomial growth condition by applying the operator decomposition method. Then, by the fractal dimension theorem of pullback attractors given by ^[6], we prove the finite fractal dimension of pullback attractors for a nonclassical diffusion equation in $H_0^1(\mathrm{\Omega })$.