Many practical physical problems can be numerically simulated by the variable coefficients Helmholtz equation with discontinuous wave number. The numerical method of the Helmholtz equation, with important theoretical and practical significance, is one of the hot research topics. Due to the discontinuity of wave number, the traditional finite difference method is usually unable to achieve the accuracy of the original difference scheme when solving Helmholtz equation with discontinuous wave number. Based on the idea of immersed interface method, a new fourth-order compact finite difference scheme is constructed  for two-dimensional coefficient Helmholtz equation with discontinuous wave number. The reliability and effectiveness of the new method are verified by numerical experiments.