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 used in system access control, healthcare, and judicial practices. However, the leakage of a user's iris feature data results in 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, maintaining the high performance of recognition systems while protecting privacy data. However, in the face of constantly changing data and environments, secure iris recognition schemes need to have effective scalability, meaning that the recognition scheme should maintain performance under new user registration. Most existing neural network-based secure iris recognition research does not consider the scalability of the scheme. To address the above issues, this paper proposes 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. 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 saves the privacy-preserving templates obtained through the TNCB method in previous tasks and replays these templates during the model training of the current task to achieve 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-IrisV4-Lamp dataset reached 68.32% and 98.49%, respectively, which is an improvement of 58.49% and 88.66% over the fine-tuning method. The analysis indicates that the GFR-SIR method has significant advantages in terms of security and model training efficiency due to not saving the data of previous tasks, while the PTR-SIR method excels in maintaining recognition performance but is inferior to GFR-SIR in terms of security and efficiency.