Fuzzing has been a popular approach in the domain of software testing due to its efficiency and capability to uncover unexpected bugs. Fuzz testing was originally developed in the days of sequential programs. With the rise of multi-core devices and increasing demand for computational efficiency, the prevalence of concurrent programming has led to a new wave of research applying fuzz testing techniques. In recent years, several fuzzers have been proposed for sequentially consistent multi-threading programs, a subset of concurrent programs, using thread interleaving semantics. However, exploration of fuzzing techniques for weak memory concurrency remains limited. This thesis presents a novel fuzzing approach for programs under weak memory models. It generates test cases as execution graphs instead of thread schedules, and performs mutations on the execution graphs to generate new test cases. We implement the fuzzer based on two state-of-the-art testing tools: C11Tester and GenMC. Different mutation strategies are explored for comparison. Benchmark results demonstrate that our fuzzer explores a broader range of execution graphs compared to naive random testing, resulting in improved bug detection.