Burning rate modulation of solid fuel can improve the performance of solid fuel ramjet over a wider altitude or Mach number envelopes. To better control the burning rate of a solid fuel, the effect of magnetic fields on the regression rate of solid fuel was experimentally and numerically investigated. In this experiment, the regression rates of polymethyl methacrylate (PMMA) rods under different types of magnetic field gradients were measured. Meanwhile, the morphological changes in the flame during combustion were recorded by a complementary metal-oxide semiconductor (CMOS) camera. The experimental results indicated that the regression rate for PMMA varies regularly with various magnetic field gradients, with rates in the range from -32.5% to 10.8%. Simultaneously, the flame structure also changes. The numerical simulation that considered both gas-phase combustion and gas-solid heat transfer produced results that were in good agreement with the experiment. The results show that the change in the regression rate is a result of the magnetic force acting on the paramagnetic and diamagnetic materials. By changing the flow field, the magnetic force can change the flame shape and temperature distribution. This alters the heat exchanged between the gas and the fuel surface and thus, changes the burning rate. It was found that the burning rate of solid fuel can be adjusted regularly by applying different types of non-uniform magnetic fields, and it may be used in the solid fuel ramjet burning rate modulation. (C) 2020 The Combustion Institute. Published by Elsevier Inc. All rights reserved.