In this paper, we propose using a propeller modulation on the transmitted signal (called sonar micro-Doppler) and different support vector machine (SVM) kernels for automatic recognition of moving sonar targets. In general, the main challenge for researchers and craftsmen working in the field of sonar target recognition is the lack of access to a valid and comprehensive database. Therefore, using a comprehensive mathematical model to simulate the signal received from the target can respond to this challenge. The mathematical model used in this paper simulates the return signal of moving sonar targets well. The resulting signals have unique properties and are known as frequency signatures. However, to reduce the complexity of the model, the 128point fast Fourier transform (FFT) is used. The selected SVM classification is the most popular machine learning algorithm with three main kernel functions: RBF kernel, linear kernel, and polynomial kernel tested. The accuracy of correctly recognizing targets for different signal-to-noise ratios (SNR) and different viewing angles was assessed. Accuracy detection of targets for different SNRs (−20, −15, −10, −5, 0, 5, 10, 15, 20) and different viewing angles (10,20,30,40, 50, 60, 70, 80) is evaluated. For a more fair comparison, multilayer perceptron neural network with two back-propagation (MLP-BP) training methods and gray wolf optimization (MLP-GWO) algorithm were used. But unfortunately, considering the number of classes, its performance was not satisfactory. The results showed that the RBF kernel is more capable for high SNRs (SNR = 20, viewing angle = 10) with an accuracy of 98.528%.