Generating robotic grasps for given tasks is a difficult problem. This paper proposes a learning-based approach to generate suitable partial power grasp for a set of tool-using tasks. First a number of valid partial power grasps are sampled in simulation and encoded as a probabilistic model, which encapsulates the relations among the task-specific contact, the graspable object feature and the finger joints. With the learned model, suitable grasps can be generated on-line given the task-specific contact. Moreover, a grasp adaptation strategy is proposed to locally adjust the specified contact in order to increase the grasp feasibility and also the quality of the final found grasp. We demonstrate the effectiveness of our approach using a 16 DOF robotic hand - Allegro Hand, on a variety of tool-using tasks.