Abstract: In order to improve their numerical stability in shock-capturing computations, upwind flux schemes are analyzed to figure out the reason causing numerical shock instability, and a new hybrid upwind flux scheme is designed based on the analyses. Numerical test cases are specifically designed, for investigating the major factors which cause numerical shock instability of upwind schemes on unstructured grids. The test cases show that, in certain circumstance, inappropriate numerical results can be produced by the coeffect of grid discretization and flow condition, affecting the stability of computation. The numerical flux of momentum equations presents significant impact on numerical shock stability. Therefore, a hybrid scheme with adaptive dissipation term of momentum fluxes is designed based on TV scheme, and extra numerical dissipation can be introduced near shock wave, suppressing numerical perturbation. Numerical results show that, the new hybrid scheme is capable to stably capture shock wave on unstructured grids and remains the numerical resolution of the original TV scheme in simulating viscous flows.