As a candidate alternative multicarrier scheme for the fifth generation (5G) communication, filter bank based multi-carrier with offset quadrature amplitude modulation (FBMC/OQAM) has better spectral containment, enhanced flexibility and higher spectral efficiency than the popular cyclic prefix orthogonal frequency division multiplexing, thus is more suitable for asynchronous fragmented spectrum access scenarios in future 5G. However, real orthogonality instead of complex orthogonality makes the channel estimation in FBMC/OQAM system challenging, especially when it is combined with MIMO. In this paper, an effective and low complexity compressive sensing based channel estimation method via Generalized approximate message passing (GAMP) algorithm was proposed for the time domain MIMO FBMC system. A Bayesian Cramer–Rao Bound-sparsity (BCRB-s) is obtained considering the sparsity constrain of the channel impulse response. Furthermore, a simplified preamble is brought out and evaluated. Simulation results demonstrate that the proposed scheme is more robust to channel frequency selectivity and always works well even in underdetermined cases. In particular, the performance of our GAMP-based method is close to the BCRB-s. It also showed that a tradeoff between complexity and spectrum efficiency can be made by adjusting the parameters of prototype filters used in FBMC/OQAM system.