This paper considered a multi-relay distributed cooperative system in which not only the source communicates with the destination, but also the relays have communication requests with the destination. In order to achieve the requirements of simultaneous communication for the source and relays, we propose a distributed cooperative system based on orthogonal frequency division multiplexing with index modulation (OFDM-IM). In this system, the relay can communicate with the destination by superimposing its own signal over the inactive subcarriers on the decoded OFDM-IM signal. Upper bounds on the bit error rates of the source and the active relay are both derived in closed form, whose tightness is verified through simulation results.