The simulation and analysis of neutronics parameters in Molten Salt Reactors (MSRs) is fundamental for the design of the reactor core. However, high-fidelity neutron transport calculations of the MSR are time-consuming and require significant computational resources. Artificial neural networks (ANNs) have been used in various industries, and in recent years are increasingly introduced in the nuclear industry. Back-Propagation neural network (BPNN) is one type of ANN. A surrogate model based on BP neural network is developed to quickly predict two key neutronics parameters in reactor core: the effective multiplication factor (keff) and the three-dimensional channel-by-channel neutron flux distribution. The dataset samples are generated by modeling and simulating different operation states of the Molten Salt Reactor Experiment (MSRE) using the Monte Carlo code. Hyper-parameters optimization is performed to obtain the optimal surrogate model. The numerical results on the test dataset show good agreement between the surrogate model and the Monte Carlo code. Additionally, the surrogate model significantly reduces computation time compared to the Monte Carlo code and greatly enhances efficiency. The feasibility and advantages of the proposed surrogate model is demonstrated, which has important significance for real-time prediction and design optimization of the reactor core.