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In mobile edge computing (MEC), mobile devices limited to computation and memory resources offload compute-intensive tasks to nearby edge servers. User movement causes frequent handovers in 5G urban networks. The resultant delays in task execution due to unknown user position and base station lead to increased energy consumption and resource wastage. The current MEC offloading solutions separate computation offloading from user mobility. For task offloading, techniques that predict the user’s future location do not consider user direction. We propose a framework termed COME-UP Computation Offloading in mobile edge computing with Long-short term memory (LSTM) based user direction prediction. The nature of the mobility data is nonlinear and leads to a time series prediction problem. The LSTM considers the previous mobility features, such as location, velocity, and direction, as input to a feed-forward mechanism to train the learning model and predict the next location. The proposed architecture also uses a fitness function to calculate priority weights for selecting an optimum edge server for task offloading based on latency, energy, and server load. The simulation results show that the latency and energy consumption of COME-UP are lower than the baseline techniques, while the edge server utilization is enhanced.