Microvascular invasion (MVI) is a critical factor for prognosis evaluation and cancer treatment. The current diagnosis of MVI relies on pathologists to manually find out cancerous cells from hundreds of blood vessels, which is time-consuming, tedious, and subjective. Recently, deep learning has achieved promising results in medical image analysis tasks. However, the unexplainability of black box models and the requirement of massive annotated samples limit the clinical application of deep learning based diagnostic methods. In this paper, aiming to develop an accurate, objective, and explainable diagnosis tool for MVI, we propose a Loopback Network (LoopNet) for classifying MVI efficiently. With the image-level category annotations of the collected Pathologic Vessel Image Dataset (PVID), LoopNet is devised to be composed binary classification branch and cell locating branch. The latter is devised to locate the area of cancerous cells, regular non-cancerous cells, and background. For healthy samples, the pseudo masks of cells supervise the cell locating branch to distinguish the area of regular non-cancerous cells and background. For each MVI sample, the cell locating branch predicts the mask of cancerous cells. Then the masked cancerous and non-cancerous areas of the same sample are inputted back to the binary classification branch separately. The loopback between two branches enables the category label to supervise the cell locating branch to learn the locating ability for cancerous areas. Experiment results show that the proposed LoopNet achieves 97.5% accuracy on MVI classification. Surprisingly, the proposed loopback mechanism not only enables LoopNet to predict the cancerous area but also facilitates the classification backbone to achieve better classification performance.