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Missing data imputation is an important research topic in data mining. The impact of noise is seldom considered in previous works while real-world data often contain much noise. In this paper, we systematically investigate the impact of noise on imputation methods and propose a new imputation approach by introducing the mechanism of Group Method of Data Handling (GMDH) to deal with incomplete data with noise. The performance of four commonly used imputation methods is compared with ours, called RIBG (robust imputation based on GMDH), on nine benchmark datasets. The experimental result demonstrates that noise has a great impact on the effectiveness of imputation techniques and our method RIBG is more robust to noise than the other four imputation methods used as benchmark.