Establishing and sustaining Metaverse service necessitates an unprecedented scale of resources. This paper considers the deployment of Metaverse service in a cloud-edge resource architecture, which can satisfy the escalating demand for Metaverse service resources while ensuring both high bandwidth and low latency. We propose a novel mechanism, named Reliable and Secure Metaverse Service (RSMS), to ensure Metaverse service reliability and security without sacrificing performance. RSMS consists of two protocols: (1) One is a blockchain-based lightweight mutual authentication protocol concerning heterogeneous Metaverse service resource nodes (RNs) dynamically joining a Metaverse service resource pool while guaranteeing their trustworthiness, which guarantees the security of Metaverse service. (2) The other is a group authentication protocol used to form and maintain a stable and secure Metaverse service group composed by RNs, which ensures the reliability and enhances the security of Metaverse service. The reliability and security of Metaverse service under RSMS are thoroughly discussed, and informal and formal security analysis are conducted. Additionally, we study the impact of RSMS on Metaverse service throughput, demonstrating its lightweight feature.