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This paper aims to investigate the nonlinear dynamic properties of a two-point and symmetrically supported pipeline bracket system coated with the damping element using an elastic-porous metal rubber. The dynamic model of the studied two-point and symmetric pipeline system was established based on impulse response matrix for accurate and reliable description on its nonlinear behaviours, e.g., energy dissipation and loss factor. The experimental verification of the developed model was performed by means of dynamic test as well as the analyses of nonlinear damping characteristics. The experimental results show a good agreement with the prediction results obtained from the proposed dynamic model. This work provides an alternative method to investigate the dynamics of pipeline vibration system equipped with a damping structure.