Understanding the probabilistic traffic environment is a vital challenge for the motion planning of autonomous vehicles. To make feasible control decisions, forecasting future trajectories of adjacent cars is essential for intelligent vehicles to assess potential conflicts and react to reduce the risk. This paper first introduces a Bayesian Long Short-term Memory (BLSTM) model to learn human drivers' behaviors and habits from their historical trajectory data. The model predicts the probability distribution of surrounding vehicles' positions, which are used to estimate dynamic conflict risks. Next, a hybrid automaton is built to model the basic motions of a car, and the conflict risks are assessed for real-time state-space transitions based on environmental information. Finally, a BLSTM-based Model Predictive Control (MPC) is built to navigate vehicles through safe paths with the least predicted conflict risk. By merging BLSTM with MPC, the designed neural-based MPC overcomes the defect that traditional MPC is hard to model uncertain conflict risks. The simulation results show that our proposed BLSTM-based MPC performs better than human drivers because it can foresee potential conflicts and take action to avoid them.