Wave-induced velocity diffusion is studied with a one-dimensional relativistic Vlasov-Poisson code. The diffusion coefficient is determined by following test electrons in the self-consistent electrostatic field formed by a narrow spectrum of electron plasma waves. The diffusion coefficient is found to be slightly larger than the quasilinear value at intermediate values of Chirikov's overlap parameter. The largest deviation is about 20 to 30%. At higher values of the overlap parameter, the diffusion is slower than quasilinear for a small number of field modes, but faster than quasilinear for a large number of the modes.