A nonlinear delay difference equation with periodic coef ficients was considered.Existence and uniqueness of initial value problem of th e equation and boundedness of that every solution were demonstrated by iterate a lgorithm and mathematical induction;the existence of a positive periodic soluti on of the equation was discussed by fixed point theorem and mathematical inducti on;sufficient condition for the global attractivity about positive periodic sol ution were obtained by using limit process and derivative method.The studies ex tend and improve the well-known results of the delay difference equation when t he coefficients is const.