Ranking as an important task in information systems has many applications, such as document/webpage retrieval, collaborative filtering and advertising. The last decade has witnessed a growing interest in the study of learning to rank as a means to leverage training information in a system. In this paper, we propose a new learning to rank method, i.e. BLM-Rank, which uses a linear function to score samples and models the pairwise preference of samples relying on their scores under a Bayesian framework. A stochastic gradient approach is adopted to maximize the posterior probability in BLM-Rank. For industrial practice, we have also implemented the proposed algorithm on Graphic Processing Unit (GPU). Experimental results on LETOR have demonstrated that the proposed BLM-Rank method outperforms the state-of-the-art methods, including RankSVM-Struct, RankBoost, AdaRank-NDCG, AdaRank-MAP and ListNet. Moreover, the results have shown that the GPU implementation of the BLM-Rank method is ten-to-eleven times faster than its CPU counterpart in the training phase, and one-to-four times faster in the testing phase.