Unmanned aerial vehicle (UAV) base stations (BSs) can help meet the dynamic traffic demand of flash mobile crowds, but user movements also pose a significant challenge on fast-tracking for avoiding service interruption. This paper presents a novel paral <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LE</b> l <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</b> ptimal dee <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</b> echo st <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</b> te netwo <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</b> k pre <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</b> iction (LEOPARD) approach that can fast and accurately learn the movement of a user equipment (UE) to reduce its impact on the link performance from the UE to the UAV-BS. Improving the current learning technique of deep echo state network (ESN), LEOPARD consists further three key optimization and learning techniques. First, we develop a Bayesian-Optimization Algorithm (BOA)-based hyper-parameters adjustment method for improving movement prediction accuracy. Secondly, the Message Passing Interface (MPI) technique is integrated into the design of LEOPARD to reduce the time complexity caused by BOA. Last, we design a Kuhn-Munkres (KM)-based matching algorithm to save the re-positioning energy consumption of multiple UAV-BSs. As shown in our simulation results, the prediction accuracy of the proposed LEOPARD, combining DeepESN, BOA, and MPI techniques, is 78% and 67% better than the state-of-the-art shallow ESN and the original deep ESN, respectively.