Summary: This paper proposes a numerical procedure for solving the nonlinear partial mixed Volterra-Fredholm integro-differential equations by two-dimensional triangular function (2D-TFs). The integration and differentiation in two-dimensional spaces have been presented for an operational matrix on triangular functions, whereas by converting the nonlinear partial mixed Volterra-Fredholm integro-differential equation to a system of algebraic by using these matrices. Some numerical examples, have been proposed to obtain the accuracy and effectiveness of the method.