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The rapid proliferation of new applications poses great challenges to the computation capability of mobile devices. To tackle this problem, computation offloading was proposed as a promising paradigm. In this paper, we consider a cellular device-to-device (D2D) mobile edge computing (MEC) system consisting of one base station (BS) deployed with an MEC server and users. We assume that a portion of users have task computation requirements and may perform local computing, MEC offloading, or D2D offloading. Further assuming that tasks can be partitioned into small-sized data and can be executed simultaneously via various computation modes, we jointly study computation offloading and resource allocation problem. To achieve efficient information interaction and task management, we first propose a joint task management architecture. Defining task execution cost as the weighted sum of task execution latency and energy consumption, we then formulate the joint optimization problem as a task execution cost minimization problem. As the formulated problem is a mixed integer nonlinear problem, which cannot be solved conveniently, we propose a heuristic algorithm that successively solves computation offloading subproblem and resource allocation subproblem by Kuhn–Munkres algorithm and Lagrangian dual method, respectively. Numerical results demonstrate the effectiveness of the proposed algorithm.