This paper applies the Cheng projection to the support vector machine (SVM) in handling missing data. In the process of handling missing data, each sample with missing values is replaced by its Cheng projection in the original space. Additionally, two classification algorithms for handling linearly separable and nonlinearly separable datasets with missing data are presented. For linearly separable datasets with missing data, Cheng kernel function is introduced, and an SVM classification algorithm that improves the linear kernel function to the Cheng kernel function is proposed. For nonlinearly separable datasets, a generalized Gaussian Radial Basis Function kernel is introduced and an SVM classification algorithm for handling missing data is given. For both algorithms, two comparative experiments are conducted to demonstrate their effectiveness.