Two alternating direction implicit difference schemes are derived for twodimensional distributed-order fractional diffusion equations. It is proved that the schemes are unconditionally stable and convergent in a discrete L 1 (L ∞ ) norm with the convergence orders O(τ 2 | ln τ | + h 2 1 + h 2 2 + α 2 ) and O(τ 2 | ln τ | + h 4 1 + h 4 2 + α 4 ), respectively, where τ, h i (i = 1, 2) and α are the step sizes in time, space and distributed order. Several numerical examples are given to confirm the theoretical results.