Unlike the visible light auto-focusing system, the infrared auto-focusing system is divided into far-to-near focusing and near-to-far focusing owing to the special imaging principle of the infrared detector. The auto-focusing functions in the two processes are based on the analysis of the characteristics of the respective focusing function curves. To this end, five targeted evaluation indexes are used: sensitivity, the width of the steep part of the focusing curve, steepness, variance of the flat part of the focusing curve, and time. The 13 typical sharpness evaluation functions that are commonly used in quantitative analysis are conducted, and an optimal function suitable for the two focusing processes is proposed. The results show that FLaplace can be used as the optimal function in the focusing process from near to far, and FLaplace and FSML can be used as the optimal function in focusing from near to far.