In order to investigate the effects of different strain levels on the low-cycle fatigue life of hydroxyl-terminated polybutadiene (HTPB) propellant, a series of fatigue tests were conducted under various combinations of strain amplitude and mean strain. The results indicate that fatigue life exhibits a decreasing trend with increasing strain amplitude and mean strain, while the effect of mean strain on fatigue life gradually weakens as the strain amplitude rises. Additionally, a distinct trend is observed at high strain levels: the higher the strain amplitude is, the lower the coefficient of variation is. Based on the fatigue life data obtained from the tests, with strain amplitude as the characteristic parameter, a mean strain function is incorporated into the classical log-log linear model, and a stepwise fitting of model parameters is implemented using the chaotic adaptive genetic algorithm (CAGA) and the least squares method. For the selection of the mean strain function, the coefficient of determination is adopted as the goodness-of-fit criterion to evaluate the modeling accuracy of the power function, exponential function, and quadratic polynomial, respectively. Ultimately, the power function is identified as the most suitable mathematical form for characterizing the mean strain effect, leading to the establishment of a low-cycle fatigue life prediction model considering both strain amplitude and mean strain. Compared with the measured fatigue lives, more than 90% of the predicted lives obtained from the proposed model fall within the two-fold scatter band, and 100% within the three-fold scatter band. This demonstrates that the model’s prediction accuracy satisfies practical engineering requirements, thereby providing reliable data support for the development of propellant damage models and the assessment of cumulative damage in solid rocket motors (SRMs).