Deformations of the primary mirror will significantly reduce the capability of a large telescope. Moreover, the aberration introduced by the deformations usually exceeds the dynamic range of a traditional wavefront sensor such as a classical Shack–Hartmann wavefront sensor (SHWFS). Although some methods have been proposed to improve the dynamic range of an SHWFS, these methods have their own limitations for the 4-meter-thin primary mirror (FMTPM) platform. In this paper, we introduce an aberration measurement method based on Hartmanngram structural information for the FMTPM. The simulation results show that the proposed method can significantly increase the dynamic range of an SHWFS compared with traditional methods and be robust to noise and spot missing situations for large aberration conditions. In addition, experiments with the FMTPM showed that for Beta Aurigae (HIP28360), active compensation based on the estimated aberration significantly improved the far-field spot-encircled energy. The peak value of the spot also increased about three times, indicating the aberration measurement accuracy of the proposed method.