In a dynamic Robot navigation system , the Robot has to deal with multiple number of moving objects in the environment simultaneously. The control loop of Robot motion planning comprising of sense-plan-act cycle has very short duration . Predicting the next instance position (Short Term Prediction) and the trajectory (Long Term Prediction) of moving objects in a dynamic navigation system is a part of sense-plan-act cycle. With increase in the number of moving objects under observation, the performance of the prediction techniques reduce gradually. To overcome this drawback, in this paper we propose a parallel motion prediction algorithm to keep track of multiple number of moving objects within the Robotic navigational environment. The implementation of parallel algorithm is done on a cluster computing setup. Performance of the algorithm is tested for different test case scenarios with detailed analysis on efficiency and speedup.