In this study, we deploy design and performance analysis in new system model using a relaying model, energy harvesting, and non-orthogonal multi-access (NOMA) network. It is called such topology as wireless powered NOMA relaying (WPNR). In the proposed model, NOMA will be investigated in two cases including single successive interference cancellation (SIC) and dual SIC. Moreover, the simultaneous wireless information and power transfer (SWIPT) technology can be employed to feed energy to relays who intend to serve far NOMA users. In particular, exact outage probability expressions are provided to performance evaluation. The results from the simulations are used to demonstrate the outage performance of the proposed model in comparison with the current models and to verify correct of derived expressions.