Large thin-walled structural parts have been widely used in aircrafts for the purpose of weight reduction. These parts usually contain various thin-walled complex structures with weak local stiffness, which are easy to deform during machining if improper cutting parameters are selected. Thus, local stiffness has to be seriously considered during the machining parameter planning. Existing stiffness calculation methods mainly include mechanics calculation methods, empirical formula methods, finite element methods, and surrogate-based methods. However, due to the structural complexity, these methods are either inaccurate or time consuming. To address this issue, this paper proposes a data-driven method for stiffness prediction of aircraft structural parts. First, machining regions of aircraft structural part finishing are classified into bottom, sidewall, rib and corner to further define the minimum stiffness of machining regions. Then, by representing the part geometry with attribute graph as the input feature, while computing the minimum stiffness using FEM as the output label, stiffness prediction is turned to a graph learning task. Thus, a graph neural network (GNN) is designed and trained to map the attribute graph of a machining region to its minimum stiffness. In the case study, a dataset of aircraft structural parts is used to train four GNN models to predict the minimum stiffness of the defined four types of machining regions. Compared with FEM results, the average percentage errors on the test set are 6.717%, 7.367%, 7.432% and 5.962% respectively. In addition, the data driven model once trained, can greatly reduce the time in predicting the stiffness of a new part compared with FEM, which indicates that the proposed method can meet the engineering requirements in both accuracy and computational efficiency.