A breed-and-burn molten salt reactor (BBMSR) using separate fuel and coolant salts has the potential to address the Generation IV objectives of fuel cycle sustainability and proliferation resistance, while overcoming the materials limitations of previous solid-fuelled breed-and-burn (B&B) designs. The advantages of molten salt reactors are combined with B&B operation to achieve high uranium utilisation with a simple, passively safe design. The BBMSR fuel salt is contained in fuel tubes resembling traditional solid fuels, but larger tube diameters can be used due to enhanced heat transfer by natural circulation of the salt inside the tube. Parametric studies are performed for various configurations of a single fuel tube to demonstrate the feasibility of B&B operation in the two-salt design. The neutronic performance is analysed, and a simple convection model is developed to determine the limiting power density so that the fuel residence time can be estimated. By using low-enriched fuel rather than natural uranium, the neutronic constraints of the BBMSR can be relaxed so that the thermal-hydraulic and economic performance may be improved.