Computational Fluid Dynamics (CFD) solvers are an important tool to predict the behaviour of fluid flows in many industrial sectors. Thereby, accelerating the solution process without compromising on geometric accuracy is a major goal in the development of numerical flow solvers and design optimization frameworks. For tackling the issue of complex geometries, this paper utilizes a graph-based machine learning approach for solving the regression problem of stationary fluid flow field prediction. Concretely, a graph convolutional network (GCN) architecture is applied and successfully predicts flow fields around geometrical different objects. As the GCN model operates on the numerical mesh directly, the exact geometry of the object as well as all other properties of the mesh are preserved. It turned out that a GCN is able to predict fluid flow fields of two-dimensional bluff-bodies and NACA airfoils, even considering predictions based on extrapolation. Furthermore, this approach is able to handle different sizes of point clouds up to 50k points. Finally, using the predicted flow field as an initial flow distribution for a CFD simulation, showed a decreased solver runtime in some cases.