Collagen fibrils are important ultrastructural elements in biological tissues providing mechanical properties of stiffenss, strength and toughness. Individual excised collagen fibrils subjected to a tensile test exhibit nonlinear rate-dependent mechanical behavior, even under small deformation. Classical visco-hyperelastic models, such as the neo-Hookean or Mooney-Rivlin hyperelastic models, complemented with a generalized Maxwell element, can sufficiently describe nonlinear stress-stretch responses at different strain-rates. However, their credibility to describe the stress-rate-strain-rate responses of an elastic body remains unknown. In contrast to hyperelasticity, hypoelasticity is subscribed to the stress-rate-strain- rate space, and thereupon introduces a new perspective to solve (visco-)elastic problems, in particular the rate-dependent nonlinear mechanics of biological tissues. This study is aimed to develop a visco-hypoelastic model to characterize the nano-mechanical behavior of individual collagen fibrils in tension, tested with Atomic Force Microscopy (AFM), with respect to different velocities. The hypoelastic response is derived using a rate-dependent formulation of the Mooney-Rivlin model, namely the time derivative of Mooney-Rivlin stress. Whereas the viscous response is governed by the dissipative strain-rate and postulated as a function of stress and strain-rate. The integrated stress and stretch are calculated under the approximation of a linear strain-rate space. Results show that the rate-dependent Mooney-Rivlin model has remarkable ability to differentiate the stress-rate strain-rate responses at different velocities. The predicted stress-stretch response of the hypoelastic model is akin to the experimental stress-stretch response at the highest velocity. In regard of the viscous response, its dependency on stress diminishes with the increase of stress level. In summary, the visco-hypoelastic model presented in this study is able to describe the mechanical behavior of individual collagen fibrils at varying velocities in both stress-stretch and stress-rate-strain-rate space. Nevertheless, further investigation is necessary to explain the observed dissipation behavior, and in this context also to inform further experiments. In addition, we aim to use and further develop the model to include also the effect of hydration collagen fibril mechanics as well as non-enzymatic cross-link density.