The Molten Salt Reactor (MSR) is one of the six advanced reactor nuclear energy systems for further research and development selected by Generation IV International Forum (GIF), which is distinguished by its core in which the fuel is dissolved in molten fluoride salt. Because fuel flow in the primary loop, the depletion of MSR is different from that of solid-fuel reactors. In this paper, an MCNP5 and ORIGEN2 Coupled Burnup (MOCBurn) code for MSR is developed under the MATLAB platform. Some new methods and novel arrangements are used to make it suitable for fuel flow in the MSR. To consider the fuel convection and diffusion in the primary loop of MSR, fuel mixing calculation is carried out after each burnup time step. Modeling function for geometry with repeat structures is implicated for reactor analysis with complex structures. Calculation for a high-burnup reactor pin cell benchmark is performed using the MOCBurn code. Results of depletion study show that the MOCBurn code is suitable for the traditional solid-fuel reactors. A preliminary study of the fuel mixture effect in MSR is also carried out.