Currently, college-going students are taking longer to graduate than their parental generations. Further, in the United States, the six-year graduation rate has been 59% for decades. Improving the educational quality by training better-prepared students who can successfully graduate in a timely manner is critical. Accurately predicting students' grades in future courses has attracted much attention as it can help identify at-risk students early so that personalized feedback can be provided to them on time by advisors. Prior research on students' grade prediction include shallow linear models; however, students' learning is a highly complex process that involves the accumulation of knowledge across a sequence of courses that can not be sufficiently modeled by these linear models. In addition to that, prior approaches focus on prediction accuracy without considering prediction uncertainty, which is essential for advising and decision making. In this work, we present two types of Bayesian deep learning models for grade prediction under a course-specific framework: i)Multilayer Perceptron (MLP) and ii) Recurrent Neural Network (RNN). These course-specific models are based on the assumption that prior courses can provide students with knowledge for future courses so that grades of prior courses can be used to predict grades in a future course. The MLP ignores the temporal dynamics of students' knowledge evolution. Hence, we propose RNN for students' performance prediction. To evaluate the performance of the proposed models, we performed extensive experiments on data collected from a large public university. The experimental results show that the proposed models achieve better performance than prior state-of-the-art approaches. Besides more accurate results, Bayesian deep learning models estimate uncertainty associated with the predictions. We explore how uncertainty estimation can be applied towards developing a reliable educational early warning system. In addition to uncertainty, we also develop an approach to explain the prediction results, which is useful for advisors to provide personalized feedback to students.