In this paper, we propose a biologically-inspired framework for robot learning based on demonstrations. The dynamic movement primitive (DMP), which is motivated by neurobiology and human behavior, is employed to model a robotic motion that is generalizable. However, the DMP method can only be used to handle a single demonstration. To enable the robot to learn from multiple demonstrations, the DMP is combined with the Gaussian mixture model (GMM) to integrate the features of multiple demonstrations, where the conventional GMM is further replaced by the Fuzzy GMM (FGMM) to improve the fitting performance. Also, a novel regression algorithm for FGMM is derived to retrieve the nonlinear term of the DMP. Additionally, a neural network based controller is developed for the robot to track the generated motions. In this network, the cerebellar model articulation controller (CMAC) is employed to compensate for the unknown robot dynamics. The experiments have been performed on a Baxter robot to demonstrate the effectiveness of the proposed methods. Index Terms-Robot learning from demonstrations, dynamic movement primitive, fuzzy Gaussian mixture model, Gaussian mixture regression, cerebellar model articulation controller, neural control.