Remaining useful life (RUL) prediction is critical for predictive maintenance of machinery. Data-driven prognostics methods centered on deep learning are attracting ever-increasing attention. However, most existing methods mainly provide point estimates about RUL without quantifying predictive uncertainty. In contrast, Bayesian models can offer a reliable framework for estimating predictive uncertainty, but these models require expensive computation cost. In this paper, we present a Bayesian framework based convolutional neural network (BCNN) that is easy to implement and can provide high-quality predictive uncertainty of RUL. The variational inference is adopted to approximate the posterior distribution over the model parameters. Then the approximating probability distribution is used for subsequent inference of newly observed data. The proposed method is validated using vibration signals obtained from the accelerated degradation of rolling element bearings. The timefrequency domain features are extracted from raw vibration signals using continuous wavelet transform. The results of the experiments show the effectiveness of the RUL prediction of machinery.