Calculation of the stress intensity factor K is a crucial and difficult task in linear elastic fracture mechanics. With the capacity to solve complex input-output problems of an underlying system, machine learning is especially useful in the calculation of K. However, when faced with complex systems, such as the firtree groove structure of a turbine disk, the dataconsuming issue has always been a thorny problem in K-solutions combined with machine learning studies for a long time. In this paper, a novel K-solution method called PA-GPR (Pool-based Active learning with Gaussian Process Regression) for the calculation of the stress intensity factor for surface cracks in the firtree groove structure of a turbine disk is proposed. Using the pool-based active learning strategy, the proposed K-solution method could make the GPR model have a great regression performance with a few samples required. In the pool-based active learning strategy analysis, the learning function based on greedy sampling is proposed to select samples with a high contribution to the training of the GPR model. The calculation of K for a semi-elliptical surface crack in the firtree groove structure is evaluated to verify the accuracy and effectiveness of the proposed method. The results show that this novel method is accurate, time-saving and effective.