Computer-aided image analysis of histopathology specimens could potentially provide support for early detection and improved characterization of diseases such as brain tumor, pancreatic neuroendocrine tumor (NET), and breast cancer. Automated nucleus segmentation is a prerequisite for various quantitative analyses including automatic morphological feature computation. However, it remains to be a challenging problem due to the complex nature of histopathology images. In this paper, we propose a learning-based framework for robust and automatic nucleus segmentation with shape preservation. Given a nucleus image, it begins with a deep convolutional neural network (CNN) model to generate a probability map, on which an iterative region merging approach is performed for shape initializations. Next, a novel segmentation algorithm is exploited to separate individual nuclei combining a robust selection-based sparse shape model and a local repulsive deformable model. One of the significant benefits of the proposed framework is that it is applicable to different staining histopathology images. Due to the feature learning characteristic of the deep CNN and the high level shape prior modeling, the proposed method is general enough to perform well across multiple scenarios. We have tested the proposed algorithm on three large-scale pathology image datasets using a range of different tissue and stain preparations, and the comparative experiments with recent state of the arts demonstrate the superior performance of the proposed approach.