Channel estimation refers to the method and process of receiving channel state information.The accuracy of channel estimation determines the performance of the receiver, so channel estimation must be carried out before equalization.Nowadays, the laser channel estimation for optics transmission becomes a key technology in free space optical communication in multiple-input multiple-output orthogonal frequency division multiplexing(FSO-MIMO-OFDM) system. Although the traditional method of compression sensing, as an effective method for channel estimation, has the ability to recover and reconstruct the original signal, it has paid a certain cost in computational complexity. A novel fast Bayesian matching pursuit(FBMP) algorithm was proposed to overcome the low reconstruction precision and high complexity of the existing methods. Through the prior model selection and approximate minimum mean squared error(MMSE) estimation of the parameter vector, the FBMP algorithm provided an efficient way to estimate the channel impulse response and was characterized by high reconstruction accuracy and low complexity. Simulation results show that the proposed method can significantly improve the performance of the system compared with the traditional compressed sensing(CS).