In this paper,a remapping-free adaptive GRP method for one dimensional(1-D)compressible flows is developed.Based on the framework of finite volume method,the 1-D Euler equations are discretized on moving volumes and the resulting numerical fluxes are computed directly by the GRP method.Thus the remapping process in the earlier adaptive GRP algorithm[17,18]is omitted.By adopting a flexible moving mesh strategy,this method could be applied for multi-fluid problems.The interface of two fluids will be kept at the node of computational grids and the GRP solver is extended at the material interfaces of multi-fluid flows accordingly.Some typical numerical tests show competitive performances of the new method,especially for contact discontinuities of one fluid cases and the material interface tracking of multi-fluid cases.