Abstract: In survival studies, the accelerated failure time (AFT) model is often applied to predict the event times. This article proposes a multiple-response AFT model that extends the AFT model to the multiple events case. It is assumed that the covariates are high-dimensional and the regression coefficient matrix is jointly low-rank and sparse. We also assume all the multivariate event times are subject to right-censoring by a common censoring variable. To estimate the coefficient matrix, a two-stage procedure is proposed. First weight the data with IPCW weights, and then use SESS algorithm to solve a sparse reduced-rank regression problem. The simulation results show that the proposed method performs well in many cases. The method is also applied to a real dataset of bone marrow transplant patients.