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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 is minimizing the mean-square distance between the received vector and the reconstructed received vector based on the estimated parameters. In each iteration, updating the parameters is based on the minimum mean square error criterion. We also present a stop criterion for the iterative algorithm. We derive the Cramer-Rao lower bounds (CRBs) of the considered multi-user joint parameter estimation. The simulation results show that our proposed algorithm converges fast and the estimation performance gradually approaches to the average CRBs (averaged over the random frequency offsets and fading channels). Our proposed method achieves a much lower computation complexity and better bit error rate performance than the existing SAGE method.