This paper presents a method based on extreme learning machine to learn motions from human demonstrations. We model a motion as an autonomous dynamical system and define sufficient conditions to ensure the global stability at the target. A detailed theoretic analysis is proposed on the constraints regarding to input and output weights which yields a globally stable reproduction of demonstrations. We solve the corresponding optimization problem using nonlinear programming and evaluate it on an available data set and a real robot. Combined with the generalization capacities of extreme learning machine, the results show that the human movement strategies within demonstrations can be generalized well.