Recently, number of studies delved into the application of Support Vector Machine (SVM) which is used in various fields to remote sensing has been rapidly increasing. The SVM was originally designed for purposes of binary classification and thus it needs to be extended to be applied to the multi-class classification. However, the SVM multi-class classifier extended for this purpose, may accompany problems in selecting items for the classification with varying accuracy of the results of classification to be depending upon classifiers and kernel functions to be employed for. Therefore, general criteria to select applicable algorithm are also needed for the practical application of the results of such multi-class classification. This study was designed to compare and find the most suitable multi-class classifier for the satellite land cover image classification in a high resolution KOMPSAT 2 image around the Expo-Science Park placed in Yuseong-gu, South Korea. The results of the study found the multi-class classifier of Crammer and Singer appeared to be superior to other classifiers in the study area. And results of the application of 4 kernel functions to such multiclass classifiers revealed the best performance of the RBF kernel function followed by those of the Polynomial and Linear ones while the Sigmoid function was lagging behind other ones.