In this study, we address the challenge of noise reduction in environments characterized by impulsive noise and missing input data in active noise control (ANC) systems, where existing algorithms often fail to deliver satisfactory results. Background noise, especially impulsive noise, poses a significant obstacle to signal processing and noise reduction. Furthermore, data loss during transmission or acquisition further complicates the noise reduction task. In this paper, a filtered-x imputation of the missing data maximum correntropy criterion (FxImdMCC) algorithm is proposed based on an imputation model, least mean square, and the maximum correntropy criterion (MCC), which can effectively reduce the impact of outliers and missing input data. The simulation results demonstrate the efficacy of the proposed FxImdMCC algorithm, which significantly outperforms existing algorithms in the context of active impulsive noise control.