With the rapid development of deep learning, iris recognition methods based on deep learning are constantly being proposed. These methods generally consist of iris segmentation and normalization to more accurately locate iris regions and reduce the impact of iris feature changes caused by pupil expansion. We propose a non-segmentation (NS) iris recognition framework based on a deep learning classification model, which directly takes a raw image as input for feature extraction and recognition without performing iris segmentation and normalization. This method outperforms other methods. We proposed a non-segmentation network (NSNet). NSNet is a convolutional neural network (CNN) based on an attention mechanism that enhances the robustness and accuracy of the network by reusing features and assigning channel attention values. In addition, while ensuring the advanced performance of the network, it uses only 31 convolutional layers to complete iris feature extraction and recognition tasks in the NS iris recognition framework. Since the deep learning classification model cannot recognize that the category of an image is an untrained image category, we proposed a dual-threshold iris framework. In the proposed framework, all untrained image categories are classified as impostor classes, and the first threshold set in the proposed framework can effectively prevent impostors and eliminate inferior images. The proposed framework is suitable for the pursuit of more accurate, more robust, and safer private iris recognition scenarios. We conduct experiments with uniform parameter settings on four publicly available databases and shows that even in the challenging situation where a raw image is used as the input image, the proposed method is still the most advanced algorithm. Moreover, a series of ablation experiments were conducted to further confirm that the proposed framework has a higher accuracy, robustness, and generalizability through verification and discussion.