This letter proposes a device-to-device (D2D) aided cooperative relaying system (CRS) using non-orthogonal multiple access (NOMA) to enhance the spectral efficiency. In addition, a power allocation strategy is proposed to achieve the maximum capacity scaling according to signal-to-noise ratio (SNR). The proposed D2D aided CRS using NOMA with the power allocation is shown to improve the achievable rate greatly compared to conventional CRSs with and without NOMA. In particular, it is proved that the sum-capacity scaling is log SNR for the proposed one, whereas (2/3) log SNR for the conventional ones.