AUSM⁺-up scheme is one of the most important schemes of ASUM-family. By introducing pressure dissipative mechanism into the convective fluxes and velocity diffusion into pressure fluxes, the convergence and robustness are remarkably improved in all Mach number regimes. However, based on an analysis of the scheme, it is found that a nonphysical phenomenon of infinite mass flux emerges when the Mach number is zero. For conquering the imperfection, the analytic solution of pressure discontinuity is obtained by the characteristic method. According to the results, the item of pressure dissipation is modified, and a new AUSM⁺-up scheme is developed. Using the new scheme, the strong discontinuity problems of shock wave, pressure discontinuity and shock wave diffraction are simulated. The Calculation results fit the theory results well.