This paper considers from the perspective of MAC layer, a throughput maximization problem of NOMA-ALOHA, ALOHA implemented over NOMA (non-orthogonal multiple access), that can decode simultaneously transmitted multiple packets via successive interference cancellation (SIC) if each of the multiple packets has a different power level from those of others. We start with a throughput optimization problem for two power levels and extend it to a problem for a general number of power levels. For the case of two power levels, we find upper and lower bounds of the maximum throughput and suggest a practical sub-optimal transmission probability whose throughput is close to the maximum. The maximum throughput of NOMA-ALOHA is at least 1.774 times higher than that of traditional slotted ALOHA in our numerical example. We extend the optimization problem into a general one with arbitrary number of power levels. We numerically analyze the performance through a relaxed problem of the original one with high complexity. Our numerical analysis shows that the maximum throughput of NOMA-ALOHA with three power levels is 2.33 times higher than simple ALOHA’s maximum throughput and that adding one power level to NOMA-ALOHA with two power levels enhances throughput at least by more than 28 percent.