A kind of direct numerical simulation method suitable for supercritical carbon dioxide jet flow has been discussed in this paper. The form of dimensionless nonconservative compressible Navier-Stokes equations in a two-dimensional cartesian coordinate system is derived in detail. High accurate finite difference compact schemes based on non-uniform grid system are introduced to solve the equations. The simulation results of the three vortex pairing phenomenon of plane mixing layer and a compressible axisymmetric jet flow field show that the discussed numerical simulation method is feasible to calculate the supercritical carbon dioxide jet fluid. And it is found that the difficulties of splitting the convective terms in conservation Navier-Stokes equations, which are brought by the supercritical carbon dioxide fluid pressure state equation, can be avoided by solving the nonconservative compressible Navier-Stokes equations.