This paper deals with a system combining orthogonal frequency di- vision multiplexing (OFDM) and interleave-division multiple access (IDMA). OFDM makes the system robust against intersymbol inter- ference, whereas IDMA combats the multiple access interference. Nevertheless, unwanted phenomena must be taken into account: 1/ carrier frequency offset (CFO) must be estimated/corrected to guarantee the orthogonality between subcarriers and hence the sym- bol detection in the system. 2/ the conventional iterative IDMA receiver, initially proposed by Ping et al., requires a priori knowl- edge of the multipath channel. Therefore, the CFO and the multipath channel must be estimated "accurately" in an OFDM-IDMA system. Our contribution is to propose a new scheme where a CFO correc- tion is no longer necessary, unlike common OFDM approaches. We show that without a CFO correction, the symbols transmitted by the different users can be recovered by modifying the conventional iterative architecture of the IDMA receiver. When considering an OFDM-IDMA network over different Rayleigh fading channels, simulation results clearly show the efficiency of the proposed algorithm in terms of estimation accuracy and bit error rate.