Abstract: A low complexity sparse Bayesian channel estimation algorithm was proposed for SC-FDE receiver. The proposed algorithm was obtained by applying the generalized mean field(GMF) inference framework to the Bayesian Hierarchical prior Model. In the GMF framework, we constrained the auxiliary function approximating the posterior probability density function of the unknown variables. The complexity of the method was reduced by blocking the auxiliary function of the sparse vectors into different sizes of groups. The original high-complexity algorithm(SC-VMP-3L) corresponds to the particular case when the auxiliary function is assigned to one single group. Finally, we applied the GMF inference framework to the Frequency Domain. Numerical results demonstrate that the proposed method has better performance than the traditional Orthogonal Matching Pursuit(OMP)sparse channel estimation algorithm in estimation precision of the channel and Bit Error Rate (BER) while it performs nearly as well as SC-VMP-3L algorithm but with much less computational complexity.