In Direction-of-arrival (DOA) estimation, the real-valued sparse Bayesian algorithm degrades the estimation performance by decomposing the complex value into real and imaginary components and combining them independently.We directly use complex probability density functions to model the noise and complex-valued sparse direction weights. Based on the Multiple measurement vectors (MMV), block sparse structure for the direction weights is integrated into the variational Bayesian learning to provide accurate source direction estimates. The proposed algorithm can be used for arbitrary array geometries and does not need the prior information of the incident signal number. Simulation results demonstrate the better performance of the proposed method compared with the real-valued sparse Bayesian algorithm, the Orthogonal matching pursuit (OMP) and l₁ norm based complexvalued methods.