The Cable-Driven Parallel Robots (CDPRs) have gained significant attention due to their high payload capacity and large workspace. When deploying CDPRs in practice, one of the challenges is kinematic modeling. Unlike serial mechanisms, CDPRs have a simple inverse kinematics problem but a complex forward kinematics (FK) issue. Therefore, the development of accurate and efficient FK solvers has been a prominent research focus in CDPR applications. By observing the topology within CDPRs, in this paper, we propose a graph-based representation to model CDPRs and introduce CafkNet, a fast and general FK solver, leveraging Graph Neural Network (GNN). CafkNet is extensively tested on 3D and 2D CDPRs in different configurations, both in simulators and real scenarios. The results demonstrate its ability to learn CDPRs' internal topology and accurately solve the FK problem. Then, the zero-shot generalization from one configuration to another is validated. Also, the sim2real gap can be bridged by CafkNet using both simulation and real-world data. To the best of our knowledge, it is the first study that employs the GNN to solve FK problem for CDPRs.