Abstract: In the problems such as blast waves or high-velocity jets, the negative density, pressure or internal energy may occur in the low density and pressure domain because of the numerical errors. The irrational values can cause blow-ups of the numerical algorithm. A high order positivity-preserving method is proposed base on rGFM method and WENO scheme for the problem. In the algorithm, the positivity-preserving Riemann solver is firstly used to solve the double shock approximate Riemann problem and the states of real and ghost fluid near the material interface are redefined by using the approximate solutions of Riemann problem. The positivity-preserving WENO scheme for ideal gas is then extended to the simulation of multi-media flow. Several numerical tests are given to verify the validity of the positivity-preserving method. Numerical results also show that the discontinuities such as interface can be captured precisely.