Selection of the optimal focusing function from a given set of focusing functions is an important issue in image-based auto-focusinging that is usually used in automatic image acquisition systems, such as automatic microscopes, vision-based micro-operating robots, etc. However, there is no quantitative index available for evaluating the performance of the focusing functions. Six quantitative evaluation index, including the width of steep part of focusing curve, the ratio of sharpness, the steepness, the variance of flat part of focusing curve, the factor of local extreme and the sensitivity are designed. These index can not only been used in the selection of optimal focusing function, but also provide theoretical basis for the design of new focusing function. Then, twelve typical focusing functions are evaluated based on the quantitative evaluation index. Results show that the variance function is the optimal focusing function in coarse auto-focusing, while the Brenner function is the optimal focusing function in fine auto-focusing.