Based on the effect of damped shear deformation on energy dissipation, a new constrained damping base for a polymer injection platform deck is proposed to reduce the excessive vibrations caused when multiple plunger pumps are jointly operated. A model for analyzing the vibration response of an I-beam-constrained damping base for a polymer injection platform with multiple plunger pumps was established using Abaqus 6.14 software and compared with rigid base and traditional rubber vibration isolators in terms of its vibration isolation performance. Furthermore, the effects of the damping material’s loss factor, the thickness of the damping layer, and the number of expansion layers on the vibration isolation characteristics of the constrained damping base were explored. This study shows that, with an increase in the damping material’s loss factor, the thickness of the damping layer and the number of extended layers, the vibration isolation performance of the constrained damping base is gradually enhanced. When the damping material’s loss factor is 1.0, the thickness of the damping layer is 20 mm, and the number of extended layers is 3, the constrained damping base’s vibration damping effect is optimized, and its vibration isolation rate becomes as high as 46.63%, which can significantly reduce the vibration response of the polymer injection platform.