The adaptive multi-pulse compression (AMPC) has been shown to successfully suppress the range-doppler sidelobes at the cost of heavy computation load. The fast adaptive multi-pulse compression (FAMPC) algorithm reduces the computation complexity of the AMPC via dimensionality reduction while it suffers noticeable performance degradation. This paper proposes a modified adaptive multi-pulse compression (MAMPC) algorithm that uses a two-stage processing scheme and implements with the gain-constraint-APC (GCAPC). The proposed method has almost identical estimation performance to the AMPC while maintains the same order of computation load as that of the FAMPC.