Prediction of dynamic features is an important task for determining the manipulation strategies of an object. This paper presents a technique for predicting dynamics of objects relative to the robot's motion from visual images. During the learning phase, the authors use Recurrent Neural Network with Parametric Bias (RNNPB) to self-organize the dynamics of objects manipulated by the robot into the PB space. The acquired PB values, static images of objects, and robot motor values are input into a hierarchical neural network to link the static images to dynamic features (PB values). The neural network extracts prominent features that induce each object dynamics. For prediction of the motion sequence of an unknown object, the static image of the object and robot motor value are input into the neural network to calculate the PB values. By inputting the PB values into the closed loop RNNPB, the predicted movements of the object relative to the robot motion are calculated sequentially. Experiments were conducted with the humanoid robot Robovie-IIs pushing objects at different heights. Reducted grayscale images and shoulder pitch angles were input into the neural network to predict the dynamics of target objects. The results of the experiment proved that the technique is efficient for predicting the dynamics of the objects.