The problem of misclassification in covariates is ubiquitous in survival data and often leads to biased estimates. The misclassification simulation extrapolation method is a popular method to correct this bias. However, its impact on Weibull accelerated failure time models has not been studied. In this paper, we study the bias caused by misclassification in one or more binary covariates in Weibull accelerated failure time models and explore the use of the misclassification simulation extrapolation in correcting for this bias, along with its asymptotic properties. Simulation studies are carried out to investigate the numerical properties of the resulting estimator for finite samples. The proposed method is then applied to colon cancer data obtained from the cancer registry at Memorial Sloan Kettering Cancer Center.