Combustion mechanisms of propellants under high pressures are necessary to solve the problems of a high burning rate pressure exponent in high-pressure solid rocket motors. In this study, the combustion characteristics of hydroxyl-terminated polybutadiene (HTPB) propellants were investigated by analyzing the burning rate, the quenched surface, and the combustion wave up to pressures of 28 MPa. The results showed that the pressure exponent presented an obvious break above 17 MPa, which increased from below 0.4 to approximately one. The characteristic pressure where the exponent break occurred decreased from 19.00 to 17.90 MPa with the increase of coarse ammonium perchlorate (AP) particles and decreased from 18.73 to 16.96 MPa with the addition of octogen. Coarse-AP particles exposed on the burning surface recessed relative to the binder below the characteristic pressure and protruded from the binder above the characteristic pressure. This finding was attributed to the difference in the local mass transfer between the gas phase and the burning surface under high pressures. An important finding of this study was the decline at the AP/HTPB interface above the characteristic pressure, indicating that the local heat transfer might play a crucial role in the pressure exponent break of HTPB propellants under high pressures.