This paper investigates a layered power allocation (PA) non-orthogonal multiple access (NOMA) scheme for device-to-device (D2D) re-laying networks, where the strategy of partial data transmission at relay nodes are adopted to improve the efficiency of resources. In addition, to satisfy different quality-of-service (QoS) requirements from multiple users, layered and grouped manners are involved. Moreover, the closed-form expressions in terms of the sum-rate (SR) and outage probability of the proposed scheme are derived for independent Rayleigh fading channels, which demonstrates our theoretical analysis. Both analytical and simulation results are provided to show the superiority of our proposed scheme compared with existing works.