Recent years the modify ghost fluid method (MGFM) and the real ghost fluid method (RGFM) based on Riemann problem have been developed for multimedium compressible flows.According to authors, these methods have only been used with the level set technique to track the interface.In this paper, we combine the MGFM and the RGFM respectively with front tracking method, for which the fluid interfaces are explicitly tracked by connected points.The method is tested with some one-dimensional problems, and its applicability is also studied.Furthermore, in order to capture the interface more accurately, especially for strong shock impacting on interface, a shock monitor is proposed to determine the initial states of the Riemann problem.The present method is applied to various one-dimensional problems involving strong shock-interface interaction.An extension of the present method to two dimension is also introduced and preliminary results are given.