Mobile edge computing (MEC) has been envisioned as an efficient solution to provide computation-intensive yet latency-sensitive services for terminal devices. In this paper, we investigate multi-user computation offloading in MEC and propose a joint optimization of offloading decisions, bandwidth and computation-resource allocations, with the objective of minimizing the total latency for completing all users' tasks. Due to the non-convexity of the formulated joint optimization problem, we identify its layer structure and decompose it into two problems, i.e·, a sub-problem and a top-problem. For the sub-problem, we propose a bisection-search based algorithm to efficiently find the optimal offloading solutions under a given feasible top-problem solution. Then, we use a linear-search based algorithm to obtain the optimal solution of the top-problem. Numerical results are provided to validate our proposed algorithm for minimizing the total latency in MEC-based multi-user computation offloading. We also demonstrate the advantage of our proposed algorithm in comparison with the conventional multi-user computation offloading schemes.