Whole slide imaging (WSI) is an emerging technology for digital pathology. The accuracy and speed of autofocusing are critical for the performance of the WSI system. This paper introduces a novel technique of deep autofocusing for WSI. Instead of mechanically adjusting the focal distance on a tile-by-tile basis, we develop a deep convolutional neural network for tile-wise autofocusing to generate in-focus images from tentative possibly defocused images. This deep autofocusing network (DAFNet) works with only two images taken at different focal distances; in contrast, traditional methods need to take, for each tile of the target ultra high-resolution pathology image, a stack of as many as 21 shots with varying focal distances. The novel architecture design of DAFNet facilitates the fusion of complementary information of the two input images of different focal distances. The proposed off-line reconstruction strategy allows high throughput scanning of sample slides done without compromising image quality, because DAFNet can rectify errors in focal distance and bring the scanned tiles back into focus by learnt non-linear dual-input blur-to-sharp mapping. Experimental results demonstrate the refocusing capability of the DAFNet method.