In recent years, learning ranking function for information retrieval has drawn the attentions of the researchers from information retrieval and machine learning community. In existing approaches of learning to rank, the sparse prediction model only can be learned by support vector learning approach. However, the number of support vectors grows steeply with the size of the training data set. In this paper, we propose a sparse Bayesian kernel approach to learn ranking function. By this approach accurate prediction models can be derived, which typically utilize fewer basis functions than the comparable SVM-based approaches while offering a number of additional advantages. Experimental results on document retrieval data set show that the generalization performance of this approach competitive with two state-of-the-art approaches and the prediction model learned by it is typically sparse.