A segmented primary mirror (PM) is an efficient solution to the problems of a monolithic PM manufacture, testing, transportation, and launch. However, the problem of the radius of curvature (ROC) matching among PM segments will arise, which if not solved will seriously degrade the final imaging quality of the system. Accurately detecting ROC mismatch among PM segments from the wavefront map is of crucial importance for efficiently correcting this kind of manufacturing error, while currently there are few related studies. Based on the inherent relation between the PM segment's ROC error and corresponding sub-aperture defocus aberration, this paper proposes that the ROC mismatch can be accurately estimated from the sub-aperture defocus aberration. Secondary mirror (SM) lateral misalignments will influence the accuracy of estimating ROC mismatch. A strategy is also proposed to reduce the influence of SM lateral misalignments. Detailed simulations are performed to demonstrate the effectiveness of the proposed method for detecting ROC mismatch among PM segments. This paper paves a road for detecting ROC mismatch using image-based wavefront sensing methods.