Selecting the right drugs for the right patients is a primary goal of precision medicine. In this manuscript, we consider the problem of cancer drug selection in a learning-to-rank framework. We have formulated the cancer drug selection problem as to accurately predicting 1). the ranking positions of sensitive drugs and 2). the ranking orders among sensitive drugs in cancer cell lines based on their responses to cancer drugs. We have developed a new learning-to-rank method, denoted as pLETORg , that predicts drug ranking structures in each cell line via using drug latent vectors and cell line latent vectors. The pLETORg method learns such latent vectors through explicitly enforcing that, in the drug ranking list of each cell line, the sensitive drugs are pushed above insensitive drugs, and meanwhile the ranking orders among sensitive drugs are correct. Genomics information on cell lines is leveraged in learning the latent vectors. Our experimental results on a benchmark cell line-drug response dataset demonstrate that the new pLETORg significantly outperforms the state-of-the-art method in prioritizing new sensitive drugs.