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Acoustic target classification and recognition is the core problem in the field of sound source recognition. However, learning from a small number of samples (low sample complexity) is a challenging problem in the application of deep neural network to acoustic target classification and recognition. In order to solve this problem, a method of small sample acoustic target recognition based on deep learning is proposed. The method combines manual design features with logarithmic Mel spectrum features, which expands the available features of deep learning model and improves the efficiency and accuracy of acoustic signal recognition. In the experimental verification, the recognition accuracy of this method is 87.6% on the test set; furthermore, the performance of the method is compared with other mainstream deep learning models with a small number of training samples. The results show that the method can achieve the same recognition accuracy with only a small amount of data, which has certain application value in the field of sound source detection.