Mobile edge computing (MEC) is a promising technique to support the emerging delay-sensitive and compute-intensive applications for user equipment (UE) by means of computation offloading. However, designing a computation offloading algorithm for the MEC network to meet the restrictive requirements towards system latency and energy consumption remains challenging. In this paper, we propose a joint user-association, task-partition, and resource-allocation (JUTAR) algorithm to solve the computation offloading problem. In particular, we first build an optimization function for the computation offloading problem. Then, we utilize the user association and smooth approximation to simplify the objective function. Finally, we employ the particle swarm algorithm (PSA) to find the optimal solution. The proposed JUTAR algorithm achieves a better system performance compared with the state-of-the-art (SOA) computation offloading algorithm due to the joint optimization of the user association, task partition, and resource allocation for computation offloading. Numerical results show that, compared with the SOA algorithm, the proposed JUTAR achieves about 21% system performance gain in the MEC network with 100 pieces of UE.