The nonlinear viscoelastic properties of the anteromedial (AM) bundle of porcine anterior cruciate ligament (ACL) were characterized by using a new analytical approach based on the quasi-linear viscoelastic theory. Stress relaxation and cyclic tensile tests were performed. Using the solution derived from this approach, we curve-fitted data from the stress relaxation test to determine the viscoelastic coefficients for the ligament bundles. The coefficients were verified by comparison of the predicted and the experimental results from the cyclic tensile test. The ACL AM bundle exhibited significant stress relaxation with time; a reduction of more than 50% of the peak value occurred during the 2-h experiment. Also, the reduced relaxation function for the ACL AM bundle was not a linear function of logarithmic time, as is commonly assumed for many soft tissues. The new approach, which takes into account the finite strain rate of the ramp function used in the stress relaxation test, provides an accurate description of this nonlinear stress relaxation behavior.