Robot Behavior Learning by Demonstration deals with the ability for a robot to learn a behavior from one or several demonstrations provided by a human teacher, possibly through tele-operation or imitation. This implies controllers that can address both (1) the feature selection problem related to a great amount of mostly irrelevant sensory data and (2) dealing with temporal sequences of demonstrations. Echo State Networks have been proposed recently for time series prediction and have been shown to perform remarkably well on this kind of data. In this paper, we introduce ESN to robot behavior acquisition in the scope of a mobile robot performing navigation tasks. ESN actually show comparable and even better performance with that of other algorithms from the literature in similar experimental conditions. Moreover, some properties regarding dynamics of ESN in the context of learning by demonstration are investigated.