Abstract The viscoelastic behavior of a concrete under dynamic and quasi-static loadings is studied. The viscoelastic behavior of the concrete under dynamic conditions is investigated by a transient wave propagation method using a pendulum impact setup, while its quasi-static behavior is investigated by a uniaxial compressive test. The results show that the concrete behaves viscoelastically under the stress wave loading, while nonlinearly elastic under the quasi-static loading. The dynamic viscoelastic moduli, i.e., the storage modulus and the loss modulus of the concrete can be divided into three portions with respect to wave frequency and the nonlinear behavior can be ignored for the stress wave propagation in the concrete. A nonlinear three-element viscoelastic model is subsequently proposed to describe the viscoelastic behavior of the concrete. The parameters of the present viscoelastic model are determined by the proposed dynamic and quasi-static test methods. The present nonlinear viscoelastic model is verified by the measured strain histories under dynamic loading and quasi-static tests, respectively. It shows that the present nonlinear viscoelastic model is capable in describing the viscoelastic behavior of the concrete with a high accuracy.