Non-orthogonal multiple access (NOMA) is considered a primary candidate addressing the challenge of massive connectivity in fifth generation wireless communication systems. In this letter, we propose a low-complexity NOMA mechanism with efficient multi-user detection (MUD) based on the adaptive alternating direction method of multipliers, which is able to jointly detect user activity and transmitted data. The proposed algorithm leverages the transmit symbol estimate and active user set as “prior knowledge,” which can be obtained from the previous iterations/time intervals, for improved MUD performance. We demonstrate that our proposed mechanism outperforms the state-of-art MUD NOMA schemes.