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Genotype imputation, where missing genotypes can be computationally imputed, is an essential tool in genomic analysis ranging from genome wide associations to phenotype prediction. Traditional genotype imputation methods are typically based on haplotype-clustering algorithms, hidden Markov models (HMMs), and statistical inference. Deep learning-based methods have been recently reported to suitably address the missing data problems in various fields. To explore the performance of deep learning for genotype imputation, in this study, we propose a deep model called a sparse convolutional denoising autoencoder (SCDA) to impute missing genotypes. We constructed the SCDA model using a convolutional layer that can extract various correlation or linkage patterns in the genotype data and applying a sparse weight matrix resulted from the L1 regularization to handle high dimensional data. We comprehensively evaluated the performance of the SCDA model in different scenarios for genotype imputation on the yeast and human genotype data, respectively. Our results showed that SCDA has strong robustness and significantly outperforms popular reference-free imputation methods. This study thus points to another novel application of deep learning models for missing data imputation in genomic studies.