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This paper proposes a novel iterative joint estimation of channels and frequency offsets for uplink OFDMA systems. The proposed method is based on the iterative line search algorithm with a trust region. The objective function minimizes the mean-square distance between the received vector and the reconstructed received vector based on the estimated parameters. In each iteration, the parameters are updated based on the minimum mean square error criterion. We also present a stop criterion for the iterative algorithm. The simulation results show the fast convergence rate of the proposed algorithm with asymptotic performance approaching the average CRBs (averaged over the random frequency offsets and fading channels). Our proposed method achieves a much lower computational complexity and better bit error rate performance than the existing SAGE method.