This study analyzed the viscoelastic properties of asphalt binders reinforced with various fibers, such as modified asphalt binder, modified asphalt binder reinforced with lignin fibers (LFs), polyester fibers (PFs), and polypropylene fibers (PPFs), using dynamic shear rheological (DSR) testing. Then, the experiment generated data on the dynamic modulus and phase angle, which described the dynamic rheological characteristics at varying temperatures. The generalized Maxwell model was employed to select the appropriate element, and the test curve was fitted into a discrete time spectrum based on the time–temperature equivalence principle (TTSP). The master curves of the relaxation modulus and creep compliance were established to predict the relaxation and creep properties of various asphalt binders. The analysis indicated that fiber-reinforced binders offer superior resistance to high temperatures and long-term deformation, while being less sensitive to temperature and having a more significant elastic characterization. The binders reinforced with PPFs and LFs exhibited superior performance in high-temperature settings and long-term durability, respectively. On the other hand, the binder reinforced with PFs displayed exceptional high-temperature elastic properties. Additionally, based on the experimental data and corresponding discussion, it appears that the 13-element GM model is more appropriate for fitting the data.