This paper presents a normal contact force approach for viscoelastic spheres of the same material based on the theory of viscoelasticity. The approach treats the normal contact force as an elastic component superposed with a dissipative component based on which to derive a reduced expression, and is numerically analyzed for the viscoelastic spheres modelled by the standard linear solid with the sinusoidal displacement history. The influences of relaxation time and viscosity upon the approach are discussed. An application of the approach with the collinear impact of viscoelastic balls is carried out and its adequacy to reality is validated by the comparison of the numerical solution against the impact experiment of Golf and Superball, to conclude that the suggested approach is applicable to build the kinematic equation describing the normal contact of viscoelastic bodies. (C) 2019 Elsevier B.V. All rights reserved.