The monogenic signal and Gaussian process model are applied to synthetic aperture radar (SAR) target recognition. The monogenic signal is used to extract the features of the SAR image. The Gaussian process model is a statistical learning algorithm based on the Bayesian theory, which constructs a classification model by combining the kernel function and the probability judgement. Compared with the traditional classification model, the Gaussian process model can obtain higher classification efficiency and accuracy. During the implementation, the monogenic feature vector of the SAR image is used as the input, and the target label is used as the output to train the Gaussian process model. For the test sample to be classified, the target label is determined by calculating the posterior probability of each class using the Gaussian process model. In the experiments, the validations are carried out under typical conditions based on the MSTAR dataset. According to the experimental results, the proposed method maintains the highest performance under the standard operating condition, depression angle differences, and noise corruption, which verifies its effectiveness and robustness.