In this paper, we jointly consider partial offloading and resource allocation to minimize the sum latency with energy efficiency for multi-user mobile-edge computation offloading (MECO) system based on orthogonal frequency-division multiple access (OFDMA). We formulate mixed integer non- linear programming (MINLP) sum latency minimization problem considering the edge execution delay, desired energy consumption for local computation, OFDMA, QoS, transmission power in uplink and edge computation capacity constraints. We propose that a user can make use of multi-channel transmissions to reduce the transmission delay for task with large data size. We first derive an expression to determine optimal offloading fraction such that edge computing delay is less than the local execution delay and energy consumed for local execution does not exceed the desired limit. Then, we transform the original problem into communication and computation resource allocation problem and propose a suboptimal low complexity algorithm to find the resource allocation. The simulation results show that the proposed scheme achieves 17% and 25% better performance than random and complete offloading schemes, respectively.