Due to the challenge and complexity of underwater imaging environment, captured underwater images often suffer from low contrast, haze, blur, and other degradations, seriously hindering their understanding and analysis. Thus, achieving image quality assessment (IQA) has become an important component in various underwater visual applications. However, most IQA metrics fail to consider the complex authentic distortions in underwater images, which are caused by the light absorption and scattering effects, resulting in limited quality prediction performance. To this end, we propose a novel no-reference underwater image quality assessment method by extracting a total of 28 features for contrast measure, sharpness measure, and naturalness measure. Technically, the contrast is measured by calculating the statistical characteristics of the contrast energy based on the human visual perception. Also, we combine the perceptual sharpness index and visual saliency to improve the accuracy of the sharpness measurement. Besides, the naturalness is represented by exploiting the spatial structure variation caused by various distortions of the underwater image. After feature extraction, we feed these quality-aware features into the support vector regression (SVR) to establish the nonlinear relationship between feature space and subjective quality score. Extensive tests and comparisons are conducted on UWIQA and UID2021 to testify the capabilities of our proposed method. Experimental results demonstrate that the proposed method achieves a strong correlation with the subjective mean opinion score, which validates its superior prediction performance. The code is available at: https://github.com/Hou-Guojia/CSN.