Learning from demonstration(LfD) allows for the effective transfer of human manipulation skills to a robot by building a model that represents these skills based on a limited number of demonstrated samples. Nonetheless, a skilllearning model that can comprehensively satisfy multiple requirements, such as computational complexity, modeling accuracy,trajectory smoothness, and robustness, is still lacking. Thus, this work aims to provide such a model by employing fuzzy systems. Particularly, we introduce an LfD model named Takagi-Sugeno-Kang fuzzy system-based movement primitives(TSKFMPs), which exploits the advantages of the fuzzy theory for effective robotic imitation learning of human movements.Our work formulates the TSK fuzzy system and gradient descent(GD) as imitation learning models, leveraging recent advancements in GD-based optimization for fuzzy systems. This study takes a two-step strategy.(i) The input-output relationships of the model are established using TSK fuzzy systems based on demonstration data. In this way, the skill is encoded by the model parameter in the latent space.(ii) GD is used to optimize the model parameter to increase the modeling accuracy and trajectory smoothness. We further explain how learned trajectories are adapted to new task scenarios through local modulation. We conduct multiple tests using an open dataset to validate our method, and the results demonstrate performance comparable with those of other models. Finally, we implement it in a real-world case study.