Non-orthogonal multiple access (NOMA) is envisioned as an efficient candidate for future communication systems. This letter proposes a novel orthogonal frequency division multiplexing (OFDM) with index modulation (IM)-based NOMA scheme, called OFDM-IM NOMA, for future multi-user communication systems. Inspired by IM and classical OFDM-NOMA, users utilize flexibility by adjusting power allocation factors and subcarrier activation ratios. Our new scheme allows different service users to share available resources as in classical NOMA, more efficiently. It is shown that OFDM-IM NOMA reliably supports a high and low data rate user at the same resources by adjusting their subcarrier activation ratios.