Stateful protocol programs are a critical component of the network systems, and vulnerabilities in these programs can lead to severe consequences. Fuzzing, as an effective testing technique, has proven to be a powerful method for discovering vulnerabilities in stateful protocol programs, thereby enhancing their reliability and security. However, current stateful protocol fuzzers often rely on randomly mutating both the content and sequence of messages, leading to two major limitations. First, constraints between states and message types impose restrictions on the valid ordering of message types. Completely random sequence mutation frequently results in test cases that are partially valid but largely discarded by the program. Second, existing methods struggle to generate new message types that do not appear in the initial seed corpus. To overcome these limitations, we propose a stateful protocol fuzzing approach that leverages constraints between states and message types. We implement this approach in a prototype tool called STCFuzz. STCFuzz begins by identifying states, message types, and their associated constraints in the program code through static analysis. It then leverages this information to perform constraint-based sequence mutation to generate more effective test cases. Additionally, STCFuzz utilizes large language models to generate new message types absent from the original seed corpus. We conduct comparative experiments between STCFuzz and other state-of-the-art fuzzers. Experimental results demonstrate that STCFuzz achieves an average improvement of 13.4% in state transition coverage and 7.7% in code coverage compared to other fuzzers. Furthermore, STCFuzz triggers more crashes and discovers more vulnerabilities, highlighting its effectiveness in uncovering security flaws.