Abstract: Aiming at the problem of task and action trajectory generalization in robot learning by demonstration, a method is proposed which combines task-parameterized learning for multi-demonstration action trajectories with action sequence reasoning. For the multi-demonstration trajectory samples of general action primitives, the dynamic movement primitives (DMPs) are used to encode trajectories and the task-parameterized model is built. Gaussian process regression is used to learn the mapping between external parameters and model parameters. Planning domain definition language (PDDL) is applied to deriving the missing action sequence for a new task instance. The task-parameterized model generalizes the target trajectories of actions according to the new external parameters and corrects the trajectory errors. Experiments on a UR5 robot show that the proposed method can generate action sequences and adjust generalization targets flexibly in the face of different task instances and changing environment. The task-parameterized model based on multi-demonstration can generalize smooth target trajectories for given external parameters with better effects compared to a single demonstration trajectory, which improves the ability of task generalization for robots.