In this paper, we investigate the job scheduling problems with human multitasking and asymmetric switching costs. It is shown that the makespan problem is binary NP-hard. Both the total completion time and the due date assignment problems are unary NP-hard. We then consider a special case in which the cost of switching from job A (interrupted job) to job B (interrupting job) is in a form of κ1 ƒpA + κ2 ƒwB, where κ1 and κ2 are constants and ƒpA and ƒwB are costs depending on job A and B respectively. With this special form of switching cost, we show that the makespan, the total completion time and the due date assignment problems can be formulated as linear assignment problems and thus be solved in polynomial time. Even if stress effect is introduced, these three scheduling problems with the special form of asymmetric switching costs are polynomial time solvable.