This article deals with a method, based on total variation diminishing (TVD) scheme, for solving three-dimensional equations of gravitational gas dynamics. For this method a parallel algorithm of the decision is o®ered. Equations of this kind are a powerful approach to simulating astrophysical problems. Numerical schemes applied for their solving must provide high-resolution capturing of shocks, prevent spurious oscillations and specify the behavior of the matter in the neighborhood of small perturbations beyond shock fronts. Difference schemes have to combine the properties of high resolution in the regions of small perturbations and of monotonicity in the domains of steep gradients in order to satisfy such contradictory conditions.