Poles assignment problem for second-order linear periodic system by using periodic proportion-plus-derivative (PD) state-feedback is considered in this paper. The poles assignment problem via periodic PD state-feedback in a class of discrete periodic second-order linear systems can be transformed into the problem of solving a class of constrained discrete periodic regulator equations. A complete parametric approach to poles assignment via periodic PD state-feedback is proposed based on the solutions to the discrete periodic regulator matrix equations. Based on the proposed parametric method, the consideration of the minimization problem and the robust problem of the plant system are proposed. Two numerical examples are presented to illustrate the effectiveness of the proposed approaches.