In present paper joint with Prof. Dr. A. Ashyralyev, the mixed boundary value problem for the multi-dimensional hyperbolic equation, is considered. Here ? is the unit open cube in the m-dimensional Euclidean space Rm {x = (x1, · · ·, xm) : 0 0 . A numerical method is proposed for solving multidimentional hyperbolic partial differential equations with nonlocal integral condition. The first and second orders of occuracy stable difference schemes are presented. The stability of these difference schemes are established. The method is illustrated by numerical examples.