In this paper, the best relay selection (BRS) is proposed for cooperative relaying system based on non-orthogonal multiple access (NOMA). Approximate and asymptotic expressions for average rate of the proposed scheme are derived under independent Rayleigh fading channels. Numerical results show that the NOMA-based BRS (N-BRS) attains more rate gain than the conventional BRS (C-BRS) when a number of relays becomes large.