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A low diffusion flux splitting method capable of capturing crisp shock profile and exact contact surface is presented. Here, the flux vector of the Euler equations is split into convective and pressure parts following Toro–Vazquez formulation. The low diffusive property of the present scheme is brought about by adding an anti-diffusion term to the pressure parts. This numerical method can be regarded as an improved version of Toro and Vazquez’s flux splitting schemes (i.e. TV and TV-AWS) which are found to produce shock instabilities and carbuncle phenomena. Numerical results for several carefully chosen one- and two-dimensional test problems are investigated to demonstrate the accuracy and robustness of the proposed scheme.