The correction of uneven illumination in microscopic image is a basic task in medical imaging. Most of the existing methods are designed for monochrome images. An effective fully convolutional network (FCN) is proposed to directly process color microscopic image in this paper. The proposed method estimates the distribution of illumination information in input image, and then carry out the correction of the corresponding uneven illumination through a feature encoder module, a feature decoder module, and a detail supplement module. In this process, overlapping residual blocks are designed to better transfer the illumination information, and in particular a well-designed weighted loss function ensures that the network can not only correct the illumination but also preserve image details. The proposed method is compared with some related methods on real pathological cell images qualitatively and quantitatively. Experimental results show that our method achieves the excellent performance. The proposed method is also applied to the preprocessing of whole slide imaging (WSI) tiles, which greatly improves the effect of image mosaicking.