This paper presents a new approach to the incremental online learning of behaviors by a robot from multiple kinesthetic teaching trials. The approach enables a robot to refine and reproduce a specific behavior every time a new teaching trial is provided and to decide autonomously whether to accept or reject each trial. The robot neglects bad teaching trials and learns a behavior based on adequate teaching trials. The framework of this approach consists of the projection of motion data to a latent space and the description of motion data in a Gaussian mixture model (GMM). To realize the incremental online learning, the latent space and the GMM are refined incrementally after each proper teaching trial. The trial data are discarded after being used. The number of Gaussian components in the GMM is not initially fixed but is autonomously selected by the robot over the trials. The proposed method is more suitable for practical human-robot interaction. The experiments with a humanoid robot show the feasibility of the approach. We demonstrate that the robot can incrementally refine and reproduce learned behaviors that accurately represent the essential characteristics of the teaching trials through our learning algorithm and that it can reject erroneous teaching trials to improve learning performance.