Supervised speech enhancement has gained significant progress from recent advancements in neural networks, especially due to their ability to non-linearly fit the diverse representations of target speech, such as waveform or spectrum. However, most of them continue to face issues with degraded speech and residual noise in challenging acoustic scenarios. In this paper, to alleviate the above issues, we propose a residual iterative voice correction framework to further correct the acoustic structure of the speech pre-enhanced by existing enhancement solutions. Concretely, inspired by the chain rule for information, we perform multiple corrections in a residual iterative manner to refine the spectral structure details of pre-enhanced speech. Experimental results on the DNS-Challenge dataset show that our solution consistently improves 0.3+ PESQ score over baselines, with only an additional 1.18 M parameters.