This paper presents a comparative investigation into behaviors of different damping terms of viscoelastic contact models, and introduces a novel damping term with dimensional reasoning analysis and by considering the effect of relaxation time of viscoelastic spheres. Behaviors of different contact models are compared in terms of predictions of non-dimensional variables, where the influence of damping parameters on behaviors of viscoelastic models is analyzed and the relationship between non-dimensional damping parameters and the coefficient of restitution is discussed. The damping parameter related to relaxation time is found to affect behaviors of the current viscoelastic contact model significantly. Viscoelastic models of different damping terms exhibit different behaviors, especially for a heavily damped case. Comparison between simulation and free fall impact test of viscoelastic balls demonstrates that the current contact model involving relaxation time fits experimental results better than other contact models. (C) 2019 Elsevier B.V. All rights reserved.