Summary: Double censoring often occurs in biomedical research, such as HIV/AIDS clinical trials, when an outcome of interest is subject to both left censoring and right censoring. It can also be seen as a mixture of exact and current status data and has long been investigated by several authors for theoretical and practical purposes. In this article, we propose the Buckley-James method for an accelerated failure time model under double random censoring. For the semiparametric inference, where the error distribution of the censored linear model is left unspecified, we develop an efficient EM-based self-consistency procedure to estimate the regression parameter and the unknown residual distribution function. Asymptotic properties, including the uniform consistency and weak convergence, are established for the proposed estimators. Simulation studies demonstrate that the proposed procedure works well under various censoring schemes and outperforms the inverse-probability weighting method in terms of accuracy and efficiency. The method is applied to the HIV/AIDS study.