A modified ghost fluid method is developed to avoid the oscillations of pressure and velocity at the interface when the original ghost fluid method (GFM) is applied to a strong shock wave impacting on a material interface. The pressure and velocity of the ghost fluid are replaced respectively by the pressure and velocity of the interface which are obtained by solving a Riemann problem, the density of the ghost fluid is gained by extrapolating the entropy constant. The modified GFM keeps to the simplicity of the original GFM. Numerical tests are carried out by using the modified GFM for a one-dimensional strong shock wave impacting on the gas-gas, gas-liquid interfaces and a jet impacting on the gas-liquid interface. The satisfactory results are achieved.