Orthogonal frequency-division multiplexing (OFDM) with subcarrier number modulation (OFDM-SNM) manifests its superior nature of high spectral efficiency (SE) and low complexity for signal estimation. To exploit the spatial gain of OFDM-SNM, we propose a relay assisted OFDM-SNM scheme for multi-hop cooperative systems in this letter. It is stipulated that a relay operated by decode-and-forward (DF) and half-duplex (HD) protocols exists in each hop. We analyze the outage performance of the relay assisted OFDM-SNM system. The average outage probability is approximated in closed form. Moreover, to reveal the diversity and coding gains of relay assisted OFDM-SNM, we explore the asymptotic outage performance at high signal-to-noise ratio (SNR) by power series expansion. To verify the improvement on outage performance and energy efficiency, we carry out the comparison among different multi-hops systems with traditional OFDM-SNM fixing a certain distance from source to destination. Simulation results corroborate the derived outage probabilities and provide insight into the proposed system in this letter.