The continuous expansion of the Internet of Things (IoT) presents increasing challenges for secure and efficient group key management, particularly in scenarios involving dynamic membership and constrained resources. While blockchain has been explored to improve decentralization and auditability, many existing schemes remain limited by high operational overhead and insufficient adaptability. This paper proposes a lightweight blockchain-based cluster key management scheme for IoT networks. Integration of Elliptic Curve Cryptography (ECC) with blockchain reduces computational complexity while enhancing security. IoT devices are organized into clusters, where head nodes serve as key distribution centers for key management and communication. Identity credentials and key parameters are securely stored on the blockchain, enabling decentralized key management without centralized control risks. Cluster dynamics are modeled via a discrete-time Markov chain. Security analysis confirms compliance with core security requirements, and performance evaluations demonstrate lower energy consumption than some existing schemes, improving applicability in resource-constrained IoT environments.