Visible light communication is a new communication method that uses the visible light band as a communication carrier and takes into account lighting and data transmission. It has the advantages of no electromagnetic interference, rich spectrum resources and so on. Combining MIMO with VLC system can improve the communication capacity and rate of the system. However, MIMO-VLC systems need channel estimation to obtain channel state information to ensure the reliability of system communication. Although the commonly used LS channel estimation algorithm has a low complexity, it requires a lot of pilot overhead, which leads to a reduction of spectrum efficiency. Compressed sensing is applied to channel estimation to reduce pilot overhead and improve channel estimation performance because it can sample signals at a rate lower than Nyquist sampling rate and has a higher reconfiguration progress. The commonly used compressed sensing reconstruction algorithm, OMP algorithm, needs to predict the sparsity of the channel, and the true sparsity of the channel is usually unpredictable, so it has limitations in practical application. The SAMP algorithm can adaptively reconstruct the channel characteristics when the channel sparsity is unknown, which solves the condition of predicting the channel sparsity, but also increases the number of iterations of the algorithm and reduces the efficiency. Aiming at the problem of slow running speed of the SAMP algorithm, this paper proposes a Prediction-sparsity Adaptive Matching Pursuit(SAMP) algorithm based on Discrete Fourier Transform(DFT). Firstly, the sparsity of the channel impulse response is preestimated by the sparsity prediction method of DFT. Taking the estimated sparsity as the initial step of the algorithm can quickly approach the real sparsity and improve the efficiency of the algorithm. Secondly, the SAMP algorithm is used to reconstruct the channel impulse response to improve the accuracy of channel estimation and ensure the reliability of system communication. According to the performance analysis of a MIMO-VLC system with 2 inputs and 2 outputs, the mean square deviation performance of the algorithm in the paper is significantly better than that of the LS algorithm. When the forward error correction code rate threshold (3.8×10^-3) is satisfied and the pilot number is 16, the algorithm in this paper improves by 2 dB compared with the LS algorithm, and by 4.5 dB when the pilot number is 32. At the same time, the bit error rate performance of the algorithm in this paper is equivalent to that of the SAMP algorithm as a whole, which shows that the sparsity prediction method based on DFT will not reduce the reliability of system communication while improving the efficiency of the system. The system bit error rate increases with the increase of modulation order M, and the performance gain of the proposed algorithm is more obvious than that of the LS algorithm with the increase of modulation order. When the error rate reaches the FEC threshold and the modulation order is M=8, the performance of the algorithm is improved by 3.5 dB compared to the LS algorithm, and by 10 dB when the modulation order is M=64. This result shows that, when the modulation order is higher, the reduction of bit error rate is more obvious, which is conducive to the improvement of system communication efficiency. For the efficiency of CS algorithm, the DFT based sparsity prediction method significantly improves the running speed of the DFT-SAMP algorithm proposed in the paper. Compared with the SAMP algorithm, the efficiency of the algorithm in the paper increases by about 68% at 16 pilots and 69% at 32 pilots.