During construction of mountain tunnels or in service, the ground behavior may show time-dependence characteristics in the acceleration stage. In such cases, in order to quickly consider the scale of displacement suppression, a method that can easily predict future displacement is required. Therefore, we proposed a structural deteriorating type of the Voigt model (called “the D-Voigt model”) that incorporates the structural deterioration mechanism into the Voigt model. When the strain increases, this model assumes that the elastic modulus of the spring and the viscosity coefficient of the dashpot decrease. Three exact solutions are derived from the constitutive equations of this model. These exact solutions can express not only the ground behavior of the deceleration/convergence stage, but also the ground behavior of the constant-velocity stage and the acceleration stage. Next, through an example of actual data from the service tunnel, it was clarified that this model can reproduce measurement results showing time-dependence characteristics in the acceleration stage and is useful as a prediction method of future displacement. At the same time, we devised a method to identify the coefficient of this model from the measurement results and clarified that it is highly effective.