Investigation in strain-softening behavior of clay is of great significance for offshore geotechnical engineering. Although several models could be used to characterize the degradation of undrained shear strength of clay with cumulative shear strain, it is necessary to improve accuracy of them. In this study, based on full-flow cyclic penetration test, an exponential strength degradation model with one parameter α is proposed, where α is the function of the fully remolded resistance factor and the ratio of initial extraction to initial penetration resistance. The reliability of the proposed model is verified by comparing indices (strength and sensitivity) calculated by it and by other existing strain-softening models. In addition, a large deformation finite element (LDFE) analysis based on the proposed model is conducted for pipe-clay interaction, and efficiency of the model is verified by comparing numerical results with centrifuge test results. The influence of α on the normalized penetration resistance were discussed, and demonstrate the necessity of accurately evaluating degradation of undrained shear strength of clay.