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Most current genotype imputation methods are model-based and computationally intensive, taking days to impute one chromosome pair on 1000 people. We describe an efficient genotype imputation method based on matrix completion. Our matrix completion method is implemented in MATLAB and tested on real data from HapMap 3, simulated pedigree data, and simulated low-coverage sequencing data derived from the 1000 Genomes Project. Compared with leading imputation programs, the matrix completion algorithm embodied in our program MENDEL-IMPUTE achieves comparable imputation accuracy while reducing run times significantly. Implementation in a lower-level language such as Fortran or C is apt to further improve computational efficiency.