This paper aims to study the deformational behaviour of tensile-type viscoelastic dampers under different earthquake excitation directions. A method for calculating the corresponding equivalent additional stiffness and damping of a self-centring-segment bridge pier is derived. Using the displacement-based seismic design method, a design method for self-centring-segment bridge piers with tensile-type viscoelastic dampers is proposed. Using the proposed method, a self-centring-segment bridge pier is designed. Based on dynamic analysis of the finite element model by OpenSees, the effectiveness of the proposed seismic design method is validated.