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 users into groups and transmitting each group's data only on some (as opposed to all) subcarriers, G-OFDM-IDMA can have much lower decoding complexity compared with conventional OFDM-IDMA while preserving the bit error probability (BEP) performance and the bandwidth efficiency. The user grouping problem is formulated into an integer linear programming problem whose suboptimal solution is proposed and compared with the lower bound. The optimization complexity issue is also addressed. Simulations are carried out to test the performance of G-OFDM-IDMA under various system configurations. It is observed that up to 80% complexity could be saved when the conventional OFDM-IDMA is substituted by G-OFDM-IDMA configured according to the suboptimal grouping solution.