We propose a sim-to-real framework for dexterous manipulation which can generalize to new objects of the same category in the real world. The key of our framework is to train the manipulation policy with point cloud inputs and dexterous hands. We propose two new techniques to enable joint learning on multiple objects and sim-to-real generalization: (i) using imagined hand point clouds as augmented inputs; and (ii) designing novel contact-based rewards. We empirically evaluate our method using an Allegro Hand to grasp novel objects in both simulation and real world. To the best of our knowledge, this is the first policy learning-based framework that achieves such generalization results with dexterous hands. Our project page is available at \url{http://dexpc.github.io}.