In frequency division duplex (FDD) massive MIMO systems, the feedback of channel state information (CSI) increases greatly with the number of antennas raising. Therefore, it is a hot-spot to research how to reduce the feedback overhead. It is considered that massive MIMO channel is sparse and in actual situation the sparsity is unknown, so the sparse adaptive matching pursuit (SAMP) algorithm is introduced to cope with these problems. Aiming at solving the shortcomings of SAMP, including the fixed step size and too much iterations, the modified SAMP (M-SAMP) is proposed in this paper. We combine the signal segmenting, the initial sparsity estimating and variable step size to reconstruct the signal quickly and accurately. The simulation results show that M-SAMP is superior than the SAMP algorithm both in reconstruction accuracy and computation time. In addition, compared with the orthogonal matching pursuit (OMP), subspace tracking (SP), and SAMP algorithms, the better normalized mean squared error (NMSE) performance of M-SAMP could be witnessed, which demonstrates the practicability of M-SAMP in massive MIMO systems.