When survival data are collected through a prevalent cohort study, the twofold problems of censoring and length-bias typically emerge. The referred sampling plan entails not only an incomplete observations scenario as it also leads to an overrepresentation of longer "length" survivals, and so both the standard product limit-estimator (Kaplan-Meier) and the Buckley-James estimator will no longer be suitable. In this article, we propose an estimator for a linear model of interest, namely the accelerated failure time model, when the available data set is subject to the twofold problems of censoring and length-bias. The proposed estimator is based on a suitable relocation of the censored observations using Vardi's non-parametric maximum likelihood estimator of the length-biased survivor function. The presented estimator is shown to be consistent under a fairly mild set of assumptions.