Abstract: In this paper, we consider a single-machine scheduling model with a given due date and learning effect processing time. The objective function is the total weighted tardiness penalty and earliness award. Our aim is to find an optimal sequence so as to minimize the objective function. As the problem is NP-hard, we give some polynomial time solvable cases of this problem. A branch and bound algorithm was given for general case of the problem based on a rapid method for estimating the lower bound.