Missing data are a common drawback that pattern recognition techniques need to handle when solving real-life classification tasks. This paper first discusses problems in handling high-dimensional samples with missing values by the Gaussian mixture model (GMM). Since fitting the GMM by directly using high-dimensional samples as inputs is difficult due to the convergence and stability issues, a novel method is proposed to build the high-dimensional GMM by extending a reduced-dimensional GMM to the full-dimensional space. Based on the extended full-dimensional GMM, two approaches, namely, marginalization and conditional-mean imputation, are proposed to classify samples with missing data in online phase. Then, the proposed methods were employed to recognize hand motions from surface electromyography (sEMG) signals, and more than 75% of classification accuracy of motions can be obtained even if 50% of sEMG signals were missing. Comparisons with normal mean and zero imputations also demonstrate the improvements of the proposed methods. Finally, a control scheme for a myoelectric hand was designed by involving the novel methods, and online experiments confirm the ability of the proposed methods to improve the safety and stability of practical systems.