In order to treat the problem of compressible multi fluid flows with Mie-Grüneisen equation of state, a general shock limiter is developed for front-tracking method. The parameter of shock limiter is selected according to the change of average conservative error and L1 error when the parameter is changing. The shock limiter is suitable for any equation of state because the expression does not contain any material-dependent parameter of the equation of state. The open and closed states of the shock limiter are analyzed. The results show that the algorithm can solve strong shock-interface interactions of compressible multi-fluid flows with general equation of state.