Two difference schemes are derived for both one-dimensional and two-dimensional distributed-order differential equations. It is proved that the schemes are unconditionally stable and convergent in an L(L) norm with the convergence orders O(τ+h+Δα) and O(τ+h+Δα), respectively, where τ, h and Δα are the step sizes in time, space and distributed-order variables. Several numerical examples are given to confirm the theoretical results.