In this paper, we propose a full-duplex relay-assisted orthogonal frequency-division multiplexing (OFDM) with index modulation system, in which a complete transmission from source to destination is forwarded by a full-duplex decode-and-forward relay. By introducing full-duplex relaying, we are able to achieve a higher end-to-end capacity, as long as the power of the residual self-interference can be mitigated to an appropriate level. To investigate the proposed system, we assume that the maximum-likelihood detection is adopted at both relay and destination for decoding the received OFDM block. Then, we derive or approximate the average outage probability, block error rate, and end-to-end capacity in a closed form. All analyses are verified by numerical results generated by Monte Carlo simulations and comparisons between half-duplex and full-duplex relaying schemes are also provided to show the performance superiority of the proposed system.