With the rapid development of information technology, security authentication technology has become a crucial safeguard for personal privacy and data security. Among them, iris recognition technology, with its outstanding accuracy and stability, is widely applied in fields such as system access control, healthcare, and judicial practices. However, once the iris feature data of a user is leaked, it means permanent loss, as it cannot be changed or revoked. Therefore, the privacy protection of iris feature data is particularly important. With the prominent performance of neural network technology in image processing, secure iris recognition schemes based on neural networks have been proposed, which maintain the high performance of recognition systems while protecting privacy data. However, in the face of constantly changing data and environments, secure iris recognition schemes are required to have effective scalability, that is, the recognition scheme should be able to maintain performance with new user registrations. However, most of the existing research on neural network-based secure iris recognition schemes does not consider the scalability of the schemes. Aiming at the above problems, the generative feature replay-based secure incremental iris recognition (GFR-SIR) method and the privacy-preserving template replay-based secure incremental iris recognition (PTR-SIR) method are proposed in this study. Specifically, the GFR-SIR method uses generative feature replay and feature distillation techniques to alleviate the forgetting of previous task knowledge during the expansion of neural networks and adopts the improved TNCB method to protect the privacy of iris feature data. The PTR-SIR method preserves the privacy-protecting templates obtained through the TNCB method in previous tasks and replays these templates during the model training of the current task to achieve the scalability of the recognition scheme. Experimental results show that after completing 5 rounds of expansion tasks, the recognition accuracy of GFR-SIR and PTR-SIR on the CASIA-Iris-Lamp dataset reaches 68.32% and 98.49% respectively, which is an improvement of 58.49% and 88.66% compared with the fine-tuning method. The analysis indicates that the GFR-SIR method has significant advantages in terms of security and model training efficiency since the data of previous tasks is not saved; while the PTR-SIR method is more outstanding in maintaining recognition performance, but its security and efficiency are lower than those of GFR-SIR.