The single-machine problem with unavailability period for slack due date is studied. Unavailability period means that the processing job is not allowed in this period. Slack due date means that the due date is equal to its processing time plus a constant, where the constant is the decision variable. The aim is to assign the slack due and minimize the objective function. The objective function includes the early work, late work and slack due date. It discusses the range of slack due date by cost coefficients, and designs a dynamic programming algorithm to solve this problem. It is prove that the optimal solution can be obtained in O((P+T－Pmin)nP2) time. Finally, a numerical example is presented to illustrate the feasibility of the algorithms.