In this paper, we propose coopera-tive relay networks with non-orthogonal mul-tiple access in order to design a near-optimal power allocation strategy. Like other next gen-eration wireless technologies, spatially mul-tiplexed transmissions are achieved by relay nodes which enables decode-and-forward re-laying of a new superposition code after recep-tion from the source. It is worth noting that, since it is hard to exactly prove the proposed PA scheme, due the fact that it is one kind of the approximate conjectures. Therefore, math-ematical and numerical methods have been used to clarify the feasibility of the proposal. Numerical results indicate that it is able to asymptotically achieve the optimal sum rate at the higher signal-to-noise ratio region with the proposed strategy applied instead of negligible performance loss.