Interfacial instability and its induced interfacial deformation and turbulent instability are widely used. In medium characteristic scale supersonic combustion, the interfacial instability enhances the mixing of fuel and combustion aids. In small characteristic scale inertial confinement fusion, the turbulent mixing induced by interfacial instability dilutes and cools the fuel twice, thus reducing the reaction rate and even causing ignition failure. In recent years, scholars at home and abroad have deeply studied the interaction between the classical planar shock wave and the phase interface from many angles, but the research on the interaction between the shock wave and the gas-liquid oblique interface is still not systematic and comprehensive. It is of great significance to explore the evolution of shock driving gas-liquid interface instability in practical engineering applications such as supersonic combustion and inertial confinement fusion. In the process of numerical simulation, VOF model is used, combined with large eddy simulation method and appropriate boundary conditions to study the evolution process of shock induced gas-liquid two-phase oblique interface deformation and turbulent mixing in two-dimensional plane. The influence of Mach number of incident shock, initial inclination angle of shock and inclined interface inclination angle on interface instability is analyzed. The results show that the Mach number of incident shock is the most important factor in the development of interface instability. Under the same conditions, compared with the other two factors, increasing the shock Mach number can significantly increase the interface deformation and the development of turbulent mixing. At the same time, the number of serrated structures on the interface increases, the forming speed is obviously accelerated, and the width of turbulent mixing zone increases obviously. In addition, with the increase of the initial angle of shock wave and inclined interface angle, the number and forming speed of serrated structure on the interface increase at the same time, and the width of turbulent mixing zone also increases.