Based on a multiple stage BGK-type collision model and the Chapman-Enskog expansion, the corresponding macroscopic gas dynamics equations in three-dimensional space will be derived.The new gas dynamic equations have the same structure as the Navier-Stokes equations, but the stress strain relationship in the Navier-Stokes equations is replaced by an algebraic equation with temperature differences.In the continuum flow regime, the new gas dynamic equations automatically recover the standard Navier-Stokes equations.The current gas dynamic equations are natural extension of the Navier-Stokes equations to the near continuum flow regime and can be used for near continuum flow study.