In long-range target detection and tracking, image clarity plays a critical role. An infrared telescope system has a long imaging distance and a short depth of field, and the image blur caused by defocusing tends to be more severe in this system. In addition, because of the atmospheric refraction, the image derived from the telescope constantly changes. This results in a low focusing success rate and low efficiency in traditional focusing algorithms. To improve both the success rate and speed of autofocus, a mountain climbing algorithmic method with a variable step size was proposed in this study. Image clarity was obtained several times, and its median was calculated to ensure image clarity accuracy. Using the mountain climbing algorithm with momentum and acceleration reduces focusing instability as well as the number of steps required for the coarse focusing process. The algorithm was applied in an actual medium-wave infrared telescope system. Experimental results revealed that the focusing steps required by the algorithm for the coarse focusing stage were reduced by 12.8%, in comparison with the traditional mountain climbing method, meeting the requirements of aninfrared telescopesystem.