Viscoelastic dampers are conventional passive vibration control devices with excellent energy dissipation performance. The fractional derivative has a simple form and high accuracy in the modelling of viscoelastic materials/dampers. The internal variables reflect the internal state evolution of materials, and are often used to analyze the deformation and thermal process of materials. In the present work, the mechanical properties of a plate-shear-type viscoelastic damper at room temperature are tested under sinusoidal displacement excitations. The impacts of frequency and displacement amplitude on the dynamic properties of the viscoelastic damper in a wide frequency domain (0.1–25 Hz) are investigated. The higher-order fractional derivative model and the temperature–frequency equivalent principle are employed to characterize the frequency and temperature influence, and the internal variable theory considering the internal/microscale structure evolutions is introduced to capture the displacement affection. The higher-order fractional derivative model modified with the internal variable theory and temperature–frequency equivalent principle (ITHF) is accurate enough in describing the dynamic behaviors of viscoelastic dampers with varying frequencies and displacement amplitudes.