To investigate the creep mechanical properties of three-component hydroxyl-terminated polybutadiene (HTPB) composite solid propellant under different temperatures and stress levels, creep mechanical performance tests were conducted at stress levels ranging from 0.072 MPa to 0.712 MPa and four temperatures (10 °C, 25 °C, 40 °C and 55 °C) using self-developed mechanical creep performance testing device, temperature and humidity environmental chamber, and a high-definition camera, et al. The strain-creep time curves and the variation of typical mechanical performance parameters with test temperature and stress level were obtained, and a master curve for the creep fracture time was established to reflect the failure properties of the propellant under wide loading conditions. The results indicate that as the stress level increases, the characteristics of the strain-creep time curve for HTPB propellant change from three stages to four stages, while increasing temperature could reduce the critical stress level at which the curve characteristics exhibit four stages. Meanwhile, this stress level decreases with an exponential trend. The initial creep compliance increases with increasing temperature and remains almost unchanged with higher stress level. When temperature or stress level increases, the creep rate and the cumulative damage degree of the propellant becomes higher, the creep fracture time is reduced, and the cumulative damage rate is accelerated. Furthermore, the fracture strain is generally only sensitive to changes in stress level and exhibits a linear increasing trend with the increase of stress level. Finally, based on the double logarithmic experimental data of creep fracture time and stress level under different temperatures, a master curve for creep rupture time of the propellant was established using the temperature-stress level equivalence principle. At the same time, exponential mathematical expressions for the master curve and temperature shift factor were obtained.