The Mg-based propellant is considered to be a promising fuel for underwater propulsion, but the mechanism of the change of the burning rate is unclear. The Mg-based propellant was divided into two parts on the basis of the BDP multi-flame model: large-size oxidizer particle and pseudo-propellant consisting of fine oxidizer and other components, and the micro steady-state combustion model of Mg-based propellant was established. Quantitatively analysis on the gas-phase multi-flame structure was performed, which focused on the effect of pressure, Mg content, and oxidizer particle size on the burning rate. This model was verified by the results of combustion experiments on ammonium perchlorate (AP) /hydroxyl‑terminated polybutadiene (HTPB) composite propellant and Mg-based propellant, and the mean absolute percentage error between the burning rate obtained from the simulation and the experimental measurements was less than 5%. Results indicated that the flame structure of Mg-based propellant exhibited typical BDP flame characteristic. As pressure increased from 1 MPa to 4 MPa, the premixed AP flame and the preliminary diffusion flame were closer to the burning surface, which enhanced the heat feedback. And accordingly, the burning rate raised from 5.93 mm/s to 9.79 mm/s. Mg content mainly affect the combustion process of the pseudo-propellant. The premixed flame above the pseudo-propellant gradually disappeared as the Mg content increased from 15% to 63%, which led the burning rate to decrease from 17.45 mm/s to 7.83 mm/s. AP particle size affected the effectiveness of the preliminary diffusion flame on the burning surface and resulted in a change in the burning rate. These findings can provide theoretical guidance for the design of Mg-based propellant formulations.