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The visual security index (VSI) is a quantized indicator for objective visual security evaluation of selectively encrypted images. One challenging problem in current research is that the performance of VSIs is highly sensitive to the extracted features and the method of similarity measurement, and it is hard to choose appropriate handcrafted features from encrypted images, as well as to find an effective similarity measurement. In this paper, we make the first attempt to present a novel convolutional neural network-based visual security index (CNNVSI). Our proposed CNNVSI is purely data-driven and trained end-to-end. We propose three specialized designs to make the approach work for encrypted low-quality images without any handcrafted features or prior knowledge about the human vision system (HVS). First, we present a patch labeling algorithm to assign each encrypted patch a visual security score. Second, we design a multiscale attention residual network (MARNet) for feature learning. Last, we propose to fuse the learned features from plain images, encrypted images and their discrepancy images. Extensive and systematic experiments are conducted on five publicly available image databases to analyze the performance of our proposed CNNVSI, and the experimental results and their analysis demonstrate that our proposed CNNVSI significantly outperforms the existing state-of-the-art methods in terms of accuracy and stability. [ABSTRACT FROM AUTHOR]