Abstract: The heterogeneous multi-core architecture takes advantage of the strengths of different architectures to execute specific types of workloads and is typically more energy-efficient and faster. However, it is very difficult to migrate to large-scale heterogeneous platforms, and large-scale parallelism will lead to a high level of complexity in software scheduling. Although there have been related studies on the DAG task model, the research on the limited preemption scheduling strategy based on the DAG task model still has some shortcomings. In this paper, we present a worst-case response time (WCRT) analysis method for typed DAG tasks on heterogeneous multi-cores under global fixed priority limited preemption scheduling, in which each vertex of the DAG is allowed to execute on only one type of core. We present a method for analyzing the schedulability of multiple DAG tasks under global fixed-priority preemption scheduling based on the latest schedulability analysis of a single DAG task. First, a method to analyze the upper bound workload of higher priority tasks is proposed. Following that, a method for analyzing the upper bound workload of lower priority tasks is proposed. A pseudo-polynomial analysis method is proposed for analyzing the upper bound of WCRT of each typed DAG task based on the state-of-the-art method for single typed DAG task analysis. The results of our experiments with randomly generated workloads indicate that our proposed method is capable of analyzing a task set in a reasonable amount of time. In addition, the results of the scheduler meet all expectations.