Dynamically crosslinked polymers have attracted considerable attention due to its potentials in wide application of polymeric materials. Current understanding on the linear rheology of dynamically crosslinked polymer mainly focuses on the coupling between the dynamics of active network chain and dissociation kinetics of crosslinking points. In this work, we establish a model to reveal the influence of chain conformations on both the linear and nonlinear viscoelasticity in the dynamically crosslinked network. The model can accurately predict two relaxation modes in linear rheology and weak strain overshoot in nonlinear oscillatory rheology in dynamically crosslinked liquid polybutadiene rubber. It is found that catalyst can accelerate disassociation reaction by increasing its rate coefficient and decreasing its activation energy, while deaccelerate association reaction by decreasing its rate coefficient and increasing its activation energy.