A mediation model explores the direct and indirect effects of an initial variable ( X) on an outcome variable ( Y) by including a mediator ( M). In many realistic scenarios, investigators observe censored data instead of the complete data. Current research in mediation analysis for censored data focuses mainly on censored outcomes, but not censored mediators. In this study, we proposed a strategy based on the accelerated failure time model and a multiple imputation approach. We adapted a measure of the indirect effect for the mediation model with a censored mediator, which can assess the indirect effect at both the group and individual levels. Based on simulation, we established the bias in the estimations of different paths (i.e. the effects of X on M [ a], of M on Y [ b] and of X on Y given mediator M [ c']) and indirect effects when analyzing the data using the existing approaches, including a naïve approach implemented in software such as Mplus, complete-case analysis, and the Tobit mediation model. We conducted simulation studies to investigate the performance of the proposed strategy compared to that of the existing approaches. The proposed strategy accurately estimates the coefficients of different paths, indirect effects and percentages of the total effects mediated. We applied these mediation approaches to the study of SNPs, age at menopause and fasting glucose levels. Our results indicate that there is no indirect effect of association between SNPs and fasting glucose level that is mediated through the age at menopause.