Natural signals and images usually have rich temporal structures, which greatly influence the performance of the compressive image fusion algorithms based multiple measurement vectors. In this paper, a new compressive image fusion algorithm was investigated based on block sparse Bayesian learning. The proposed algorithm used a probabilistic approach, and constructed the temporal structures of images via the positive definite matrices under the multiple measurement vectors model. Thus, the MAP estimate of original images were obtained according to the Bayes rule and the estimation of hyperparameters. To verify the applicability of the proposed method, numerical experiments of image fusion were performed. Numerical results indicate that the proposed method can obviously reduce the sampling number required, and provide better fusion performance for many kinds of images compared to algorithms based on single measurement vector model.