［Purposes］Total weighted tardiness problems can be computed by the completion time of jobs after their due date. ［Methods］It studies two-agent scheduling problems with fixed time windows on a single machine, the objective function is to minimize the total weighted tardiness of the first agent. Two agent scheduling problem means that each agent has its job set, in which it can be processed in the common machine, and is used to minimize the its objective function. Assume that jobs of the first agent is preempted, there exists an agreeable condition for due date and release date. ［Findings］The jobs of the second agent are processed in some fixed due date window. ［Conclusions］By the block principle, the time complexity of the proposed problem is put forward and a pseudo-polynomial time dynamic programming algorithm is presented when a fixed time window equals the processing time.