In realistic mobile ad-hoc network scenarios, the hosts usually travel to the pre-specified destinations, and often exhibit non-random motion behaviors. In such mobility patterns, the future motion behavior of the mobile is correlated with its past and current mobility characteristics. Therefore, the memoryless mobility models are not capable of realistically emulating such a mobility behavior. In this paper, an adaptive learning automata-based mobility prediction method is proposed in which the prediction is made based on the Gauss-Markov random process, and exploiting the correlation of the mobility parameters over time. In this prediction method, using a continuous-valued reinforcement scheme, the proposed algorithm learns how to predict the future mobility behaviors relying only on the mobility history. Therefore, it requires no a prior knowledge of the distribution parameters of the mobility characteristics. Furthermore, since in realistic mobile ad hoc networks the mobiles move with a wide variety of the mobility models, the proposed algorithm can be tuned for duplicating a wide spectrum of the mobility patterns with various randomness degrees. Since the proposed method predicts the basic mobility characteristics of the host (i.e., speed, direction and randomness degree), it can be also used to estimate the various ad-hoc network parameters like link availability time, path reliability, route duration and so on. In this paper, the convergence properties of the proposed algorithm are also studied and a strong convergence theorem is presented to show the convergence of the algorithm to the actual characteristics of the mobility model. The simulation results conform to the theoretically expected convergence results and show that the proposed algorithm precisely estimates the motion behaviors.