To address accuracy issues for direct numerical simulation, a hybrid scheme based on the weighted compact scheme (WCS) and weighted essentially non-oscillatory (WENO) scheme is developed. The new hybrid method incorporates the advantages of both schemes. Time integration is performed using the fourth-order total variation diminishing Runge–Kutta method with a characteristic filter. The accuracy of the scheme is assessed using several benchmark problems. Results show that the proposed scheme produces a more accurate solution for problems involving shocks and discontinuities in comparison with the traditional shock-capturing methods.