In the present study, the mechanical behavior of tricuspid valve (TV) chordae tendineae tissue is investigated experimentally and theoretically. A series of uniaxial mechanical testing experiments of the TV chordae tendineae is conducted and its viscoelastic model is developed by taking into account the initial condition of displacement of the tissue. Our experimental result shows the typical J-shaped force-displacement curve of the TV chordae tendineae and the corresponding viscoelastic model is established via a nonlinear spring is installed to replace the linear spring of the generalized Kelvin model. In addition, specified arrangements of the model parameters and the initial condition of the individual Kelvin element are proposed. The exact solutions of the model under step-wise and constant-rate forces are analytically derived and calibration of the model constants is addressed. The resulted simulation is compared with uniaxial mechanical testing of the TV chordae tendineae tissue and shows superior performance of the proposed model under creep and monotonic loading experiments. Furthermore, the sensitivity analysis and the parameter study of the model parameters are performed to examine the influence of initial conditions of displacement as well as other internal variables on the model response under step-wise and constant-rate forces.