To research the thermal safety problem of AP/HTPB composite solid propellant under the action of thermal loading, a two-dimensional simplified model about cook-off of solid rocket motor was established. Among them, the process of slow cook-off for AP/HTPB propellant was described by using two-step global reactions. The theoretical calculation results were in good agreement with the experimental data. On this basis, the numerical predictions of slow cook-off behavior for the motor were conducted at heating rates of 1.8, 3.6 K·h^-1 and 7.2 K·h^-1, respectively. Results show that with different of heating rates, the initial ignition locations of AP/HTPB propellant are occurred in the annular region on the inner wall of the propellant at the longitudinal distance of about 1mm, and the initial ignition location moves from the central to the grain shell end surface with the increase of heating rate. When the heating rate increases from 1.8 K·h^-1 to 7.2 K·h^-1, the ignition temperature increases from 592 K to 595 K, revealing a little temperature change, but the ignition delay time shortens from 31.48 h to 14.87 h.