An important feature of Nyberg-Rueppel type digital signature algorithms is message recovery, this signature algorithm can recover the original information from the signature directly by the verifier in the verification phase after signing the message. However, this algorithm is currently vulnerable to quantum attacks and its security cannot be guaranteed. Number Theory Research Unit (NTRU) is an efficient public-key cryptosystem and is considered to be one of the best quantum-resistant encryption schemes. This paper proposes an NTRU-like message recoverable signature algorithm to meet the key agreement requirements in the post-quantum world. This algorithm, designed for the Internet of Things (IoT), constructs a secure system using the Group-Based Message Recoverable Signature Algorithm (NR-GTRU), by integrating a Group-Based NTRU-Like Public-Key Cryptosystem (GTRU) with an efficient Nyberg-Rueppel type of NTRU digital signature algorithm (NR-NTRU). This signature algorithm, resistant to quantum algorithm attacks, offers higher security at the cost of a slight efficiency reduction compared to traditional NTRU signature algorithms, and features Nyberg-Rueppel message recovery, making it well-suited for IoT applications.