This letter considers delay minimization for offloading in a mobile edge computing network with multiple users. We first show that under the same power constraint, using non-orthogonal multiple access (NOMA) can reduce the overall delay compared with time-division multiple access (TDMA). However, in this case, NOMA also consumes more energy. To ensure a fair comparison, we also consider the case when NOMA and TDMA are constrained by the same energy. Depending on the available energy, three scenarios are identified, and the corresponding optimal strategies are introduced. Simulations are conducted, showing that the proposed NOMA scheme can achieve substantial delay reduction compared with TDMA.