Abstract: Firstly, a one-field generalized Hamilton-type quasi-variational principle for linear elastodynamics with damping is proposed in this paper. This principle can fully characterize the initial-boundary value problem of elastodynamics. Based on this Hamilton-type quasi-variational principle, a time-subdomain method is presented by applying the fifth-order B-spline function as interpolation to the time subdomair Numerical results prove that the accuracy and the computational efficiency of the new method for dynamical response analysis excel obviously those of widely used Wilson-θ method and Newmark-β method.