In this paper, we have introduced a computational method for a class of two-dimensional nonlinear Volterra integral equations, based on the expansion of the solution as a series of Haar functions. To achieve this aim it is necessary to define the integral operator. The Banach fixed point theorem guarantees that under certain assumptions this operator has a unique fixed point, we have introduced an orthogonal projection and by interpolation property, we have achieved an operational matrix of integration. Also, by using the Banach fixed point theorem, we get an upper bound for the error of our method. Since our examples in this article are selected from different references, so should be the numerical results obtained here can be compared with other numerical methods.