As an emergent computing paradigm, mobile edge computing (MEC) can provide users with strong computing, storage, and communication services by moving the server to the user side. In recent years, applications such as virtual reality and augmented reality have brought higher requirements on transmission and computing capabilities. However, in the traditional cellular-based MEC, users at the edge of the cell will suffer severe signal attenuation and inter-cell interference, leading to a great reduction in achievable rate and proneness to transmission outage and offloading failure. To overcome this limitation, we combine the user-centric network (UCN) with MEC computing services and propose a novel framework called user-centric MEC (UCMEC). Through the dense deployment of access points, UCMEC can provide users with efficient, reliable, low-cost user-centric wireless transmission and edge computing services. To further exploit the benefits of UCMEC, we jointly optimize the task partition, transmit power control, and computing resource allocation decision to minimize the total energy consumption under delay constraints. Simulation results show that our proposed optimization scheme can bring users lower energy consumption and delay, and higher successful offloading probability than traditional MEC.