In radio communications, the need for recognizing the modulation type of the signals is increasing for its main role in the radio monitoring stations specifically for the electronic warfare field. This paper focuses on classifying some types of modulations, namely BPSK, QPSK, CPFSK, 4PAM and AM-DSB using support vector machines (SVMs) algorithm based on the high order cumulants (HOC). The two main phases of this classification approach are feature extraction and classifier training and testing. The feature extraction is carried out based on high order cumulants. Those features are the first, the second, the fourth and the sixth order moments. Using this extracted set of features a feature vector is constructed for each signal and a radial basis function support vector machine (RBF-SVM) algorithm is trained and its hyper-parameters are tuned to get the best of its performance. The results show a high accuracy of classification among the test signals under different values of signal-to-noise ratio (SNR) down to -20 dB.