A generalized version of orthogonal frequency division multiplexing interleave division multiple access (OFDM-IDMA) referred to as grouped OFDM-IDMA (G-OFDM-IDMA) is introduced in this paper. By dividing the users into several groups and transmitting each group's data only on part of the subcarriers, the G-OFDM-IDMA system is capable of having much lower decoding complexity compared with the conventional OFDM-IDMA while preserving the bandwidth efficiency and the bit error rate (BER) performance. We study the performance of the proposed scheme in terms of the decoding complexity and diversity order. We also extend the results to the multiple receive antennae case. Simulations are performed to corroborate the performance of the proposed G-OFDM-IDMA.