Chromosome classification is critical for karyotyping in abnormality diagnosis. To expedite the diagnosis, we present a novel method named Varifocal-Net for simultaneous classification of chromosome's type and polarity using deep convolutional networks. The approach consists of one global-scale network (G-Net) and one local-scale network (L-Net). It follows three stages. The first stage is to learn both global and local features. We extract global features and detect finer local regions via the G-Net. By proposing a varifocal mechanism, we zoom into local parts and extract local features via the L-Net. Residual learning and multi-task learning strategies are utilized to promote high-level feature extraction. The detection of discriminative local parts is fulfilled by a localization subnet of the G-Net, whose training process involves both supervised and weakly supervised learning. The second stage is to build two multi-layer perceptron classifiers that exploit features of both two scales to boost classification performance. The third stage is to introduce a dispatch strategy of assigning each chromosome to a type within each patient case, by utilizing the domain knowledge of karyotyping. The evaluation results from 1909 karyotyping cases showed that the proposed Varifocal-Net achieved the highest accuracy per patient case (%) of 99.2 for both type and polarity tasks. It outperformed state-of-the-art methods, demonstrating the effectiveness of our varifocal mechanism, multi-scale feature ensemble, and dispatch strategy. The proposed method has been applied to assist practical karyotype diagnosis.