This paper proposes the SEPS-AKA, a secure authentication and key agreement scheme for LTE-A networks, which aims to enhance security by preventing the disclosure of the International Mobile Subscriber Identity (IMSI) as clear text. The scheme utilizes public key cryptography, nonce generation, and RSA computation for secure communications without requiring changes to the existing LTE-A infrastructure. Evaluation results indicate that SEPS-AKA effectively meets security requirements such as privacy, authentication, confidentiality, and integrity for LTE-A subscribers.