Sparse Bayesian learning (SBL) has high computational complexity associated with matrix inversion in each iteration. In this paper, we investigate complexity reduced multiple-measurement vector (MMV) based implementation for single-measurement vector SBL problems. For problems with special structured sensing matrices, we propose two sub-optimal SBL schemes with significantly reduced complexity and slight estimation performance degradation, by exploiting the deterministic correlation in the converted MMV model explicitly. Two application scenarios on channel estimation in multicarrier systems and direction of arrival estimation are presented. Simulation results validate the effectiveness of the schemes.