This paper introduces an improved filtering operator based on the first-order derivative Gaussian filtering operator. As the defocus distance decreases, the edges of an image transition from being smooth to sharp. Using the operator proposed in this study, a parameter can be obtained to quantify the degree of edge sharpness, where a smaller value indicates sharper edges. By using the characteristic, we can judge whether the object is near the focal plane. Combining this information, we proposed two focus method. Both of them can avoid the problem of the hill climbing algorithm locating at local extremum points and one of them can locate the watershed between “coarse search” and “fine search” before the sharpness value crosses the peak value, so as to realize the transition from “coarse search” to “fine search” before crossing the peak value and improve focusing efficiency. This is different from previous passive focusing strategies. The final experiment shows that the proposed solutions in this paper is effective. However, the methods proposed in this study are only applicable to incoherent optical microscopy imaging systems and are not suitable for coherent light source microscopy imaging systems. Besides, the prerequisite for the successful implementation of the two proposed focusing strategies in this study is that the target exhibits sharp edges when it is within the focal plane.