A linear support vector machine (LSVM) is based on determining an optimum hyperplane that separates the data into two classes with the maximum margin. The LSVM typically has high classification accuracy for linearly separable data. However, for nonlinearly separable data, it usually has poor performance. For this type of data, the Support Vector Selection and Adaptation (SVSA) method was developed, but its classification accuracy is not very high for linearly separable data in comparison to LSVM. In this paper, we present a new classifier that combines the LSVM with the SVSA, to be called the Hybrid SVM and SVSA method (HSVSA), for classification of both linearly and nonlinearly separable data and remote sensing images as well. The experimental results show that the HSVSA has higher classification accuracy than the traditional LSVM, the nonlinear SVM (NSVM) with the radial basis kernel, and the previous SVSA.