The aim of the paper is to investigate the evolution law of burning in high explosive (HE) cracks under confinement, obtain the characteristics of convective burning in typical explosive cracks, and deepen our mechanism understanding on the process for high intensity reaction of projectile fillings under accidental ignition. The propagation of burning in preformed cracks inside octogen(HMX)-based polymer bonded explosive (PBX)(with a content of 95% for HMX) under thermal initiation was recorded by high-speed camera and pressure transducers. It is found that convective burning in 50 μm wide crack of HE under confinement can produce high pressure exceeding 250 MPa with the burning wave speed exceeding 400 m·s^-1. Comparison between crack widths reveals that with the increase of crack width, the peak pressure attributed to convective burning decreases but the burning wave speed increases. Detailed analysis of experimental data reveals that there are four stages in the evolution of convective burning in explosive cracks. The first stage is the early stage transportation of initial reaction products through crack under relatively low pressure gradient without burning on HE surface. The second stage is the steady convection of product gases with pressure growing due to combustion inside crack. The third stage is the rapid pressurization due to violent burning of HE with fracture of HE and deformation of the confinement shell. The fourth stage is the confinement failure process under extremely high pressure.