Streamline is one of the main methods of flow visualization. In light of a large amount of computation, the streamline generation from large flow fields usually requires parallel computing environments, such as high-performance computers and parallel algorithms, to accelerate computation. As wider application of heterogeneous computing systems, we design a hybrid parallel streamline generation system suitable for heterogeneous clusters in terms of data decomposition, overlapping and communication strategy with technologies such as data-parallel primitives and message passing interface to maximize the computing power of the heterogeneous parallel computing environment and achieve more efficient parallel streamline generation. A set of algorithms related to parallel particle advection are proposed and implemented. The system is deployed on a domestic supercomputer, and experiments are conducted to visualize the results of a large-scale CFD flow field simulation. This study provides relevant experimental results and analyzes the performance, scalability, and load balance of the core parallel algorithm, verifying the effectiveness and scalability of the system and algorithm.