Grouting has been widely employed to mitigate geohazards in underground projects (e.g., the tunnel). However, few studies have focused on the effects of the creep behavior of a grouting-reinforced body on the stability of tunnel operation. In this study, the curtain grouting-reinforced Nanshibi tunnel was adopted as an example to explore this issue. More specifically, uniaxial compressive creep tests were firstly performed to study the time-dependent behavior (i.e., the creep behavior) of the grouted specimen. Then, the improved nonlinear Burgers model was proposed to characterize the observed creep behavior of the grouted specimen. Finally, a numerical simulation of the tunnel operation post grouting was conducted using the newly-proposed nonlinear Burgers model. The following results were obtained: (1) The creep behavior of the grouted specimen under different loadings undergoes three stages: decaying creep, steady creep, and accelerated creep. The steady creep rate is attributed to the homogeneity of the grouting-reinforced body. (2) The nonlinear Burgers model can reasonably quantify the creep behavior of the grouting-reinforced body. (3) The creep behavior of the grouting circle of the tunnel has a significant influence on the tunnel deformation and thus the lining safety. More specifically, the tunnel deformation exhibits nonlinear growth and mainly occurs at the vault and inverted arch. Furthermore, owing to the shape of the lining structure, the arch spring is most vulnerable to cracking under the eccentric tension state. The improved creep model is proved to more accurately predict the structural deformation of a curtain grouting-reinforced tunnel. As such, it can help devise grouted-tunnel maintenance strategies for long-term safety.