In the modern era of advanced medicine, often a fraction of patients might be cured from a disease and hence the survival probability may plateau at a non-zero value and a cure rate model is needed to capture such survival fractions. A semiparametric accelerated failure time (AFT) cure model is developed for time-to-event data with a positive surviving fraction. The error distribution of the AFT model for susceptible subjects is expressed as a nonparametric mixture of normal densities which can approximate an arbitrary distribution satisfying mild regularity conditions. A Bayesian inferential framework leads to efficient estimation of the posterior distribution of parameters. Posterior consistency of the proposed estimator is established under some regularity conditions providing large sample justification of the proposed model. Markov chain Monte Carlo methods are used to generate samples from the posterior distribution of the regression coefficients to aid statistical inference. Simulation studies are conducted to evaluate the performance of the proposed model in finite samples and an analysis of breast cancer data is also presented to illustrate the method.