This study investigates the stress-strain relationship of ligament under compression at different strain rates and construct a constitutive model, providing reference for ligament injury prediction and the study of replacement materials. Materials and methods The compressive mechanical properties and compressive relaxation responses of rabbit patellar ligament under different strain rates were tested by universal tensile testing machine, and the corresponding constitutive equations were constructed. Results The uniaxial unconfined compression experiment showed that the stress and tangent modulus under 30% strain and 40% strain increases obviously with the increase of strain rate. Compared with the Gent model, the Fung and Ogden models are more suitable for fitting the ligament compression curves, and the R-squared is greater than 0.99 at the four strain rates. Four terms of Prony series are more suitable for fitting the relaxation curves of the ligaments, and the R-squared at four strain rates are all greater than 0.99. Conclusions The compressive mechanical properties of the rabbit patellar ligament demonstrate the significant viscoelastic response. The Fung and Ogden models can be used to fit the compression response of the ligament, and the four Prony series can be used to fit the compression relaxation response of the rabbit patellar ligament.