The existing collaborative filtering recommendation algorithm has the defect of sparse score matrix. To solve this problem, a recommendation algorithm based on low-rank matrix completion is proposed. By applying the variational Bayesian framework, a hierarchical Gaussian prior model was adopted to encourage a low-rank solution. To avoid cumbersome matrix inverse operations and improve computing speed, the generalized approximate message passing technique was used and embedded in the variational Bayesian framework. Meanwhile, the damping is introduced into the algorithm to promote convergence. The experiments of open datasets show that the proposed method can achieve better prediction accuracy compared with the related matrix completion algorithm.