Nowadays, the hyperspectral remote sensing imagery HSI becomes an important tool to observe the Earth's surface, detect the climatic changes and many other applications. The classification of HSI is one of the most challenging tasks due to the large amount of spectral information and the presence of redundant and irrelevant bands. Although great progresses have been made on classification techniques, few studies have been done to provide practical guidelines to determine the appropriate classifier for HSI. In this paper, we investigate the performance of four supervised learning algorithms, namely, Support Vector Machines SVM, Random Forest RF, K-Nearest Neighbors KNN and Linear Discriminant Analysis LDA with different kernels in terms of classification accuracies. The experiments have been performed on three real hyperspectral datasets taken from the NASA's Airborne Visible/Infrared Imaging Spectrometer Sensor AVIRIS and the Reflective Optics System Imaging Spectrometer ROSIS sensors. The mutual information had been used to reduce the dimensionality of the used datasets for better classification efficiency. The extensive experiments demonstrate that the SVM classifier with RBF kernel and RF produced statistically better results and seems to be respectively the more suitable as supervised classifiers for the hyperspectral remote sensing images. Keywords: hyperspectral images, mutual information, dimension reduction, Support Vector Machines, K-Nearest Neighbors, Random Forest, Linear Discriminant Analysis.