Aiming at the problem that existing centrifugal pump cavitation state recognition models over-rely on a large number of samples to achieve high recognition accuracy, a method combining a deep residual shrinkage network with a Transformer (DRSN-Transformer) is proposed. This method suppresses noise and enhances feature sparsity through soft threshold operations in DRSN, uses the DRSN layer to extract preliminary features, and uses the self-attention mechanism of the Transformer encoder to capture global features. Finally, classification is completed through the fully connected layer and Softmax classifier. Experimental results show that the average recognition accuracy of the DRSN-Transformer model for the four states of non-cavitation, incipient cavitation, cavitation development and critical cavitation in small sample scenarios is 95.06%, which is 3.22%, 13.07% and 17.34% higher than the DRSN, ResNet and CNN models respectively. This research provides an effective method for identifying cavitation states of centrifugal pumps under small sample conditions.