To solve the low channel estimation performance of LED communication system, a visible light communication system which combines the orthogonal frequency division multiplexing (OFDM) system with the multiple input multiple output (MIMO) technology and its adaptive channel estimation based on signal-to-noise ratio (SNR) are proposed. The critical threshold of SNR is determined when the five algorithms, i.e., least squares (LS), minimum mean square error (MMSE), least squares-discrete Fourier transform (LS-DFT), minimum mean square error-discrete Fourier transform (MMSE-DFT) and distributed compressed sensing synchronous orthogonal matching pursuit (DCS-SOMP), are analyzed. When SNR is lower than the critical threshold, the MMSE-DFT algorithm is used for the channel estimation, and when SNR is higher than the critical threshold, the DCS-SOMP algorithm is applied to the data reconstruction and the recovery of channel impulse response matrix. Simulation results show that when SNR is 1 dB~40 dB the proposed algorithm can reduce the mean square error (MSE) from 2.95 dB to 15 dB, and improve the LED communication quality.