Quantile regression offers great flexibility in assessing covariate effects on event times, thereby attracting considerable interests in its applications in survival analysis. However, currently available methods often require stringent assumptions on the censoring mechanism or residual distribution, or complex algorithms, which may complicate both theoretical arguments and inferences. In this paper we develop a new quantile regression approach for survival data subject to conditionally independent censoring. The proposed martingale-based estimating equations naturally lead to a simple algorithm that only involves minimizations of L1 type convex functions. We establish uniform consistency and weak convergence of the resultant estimators. Inferences are developed accordingly, including hypothesis testing, second-stage inference, and model diagnostics. We evaluate the finite-sample performance of the proposed methods via extensive simulation studies. An analysis of a recent dialysis study illustrates the practical utility of our proposals.