Modulation recognition of underwater communication signals is a critical aspect of underwater information confrontation. However, the current deep learning-based methods for underwater communication modulation recognition often mimic neural network architectures used in image processing and speech processing, tending to perform poorly in low signal-to-noise ratio (SNR) conditions. This paper introduces a novel approach by utilizing neural architecture search (NAS) method. By automatically searching for neural architectures that are well-suited for modulation recognition in underwater environment, our proposed method improves the classification performance particularly in low SNR conditions. Furthermore, we have also proposed a recognition method based on attention mechanism and feature fusion, which substantially enhances the accuracy of identifying phase-modulated signals. Numerical simulation and experimental data are used to demonstrate performance of proposed methods.