This paper investigates a variant scheduling problem of minimizing makespan in a two-machine flow shop. In this variant, there will be two tasks for each job. The first task can be processed on either machine, and the second task can only be processed on the second machine after the first task has been finished. Furthermore, if the second task should start right after the first task is completed, it is called a no-waited case and is denoted by NSHFS. On the other hand, if the second task is allowed to be processed at any time after the first task is completed, the problem is then denoted as SHFS. In the case of SHFS, based on the result of Wei and He, an improved polynomial time approximation algorithm with worst-case ratio of 8/5 is presented. In the case of NSHFS, this paper shows that it is NP-hard, and presents a polynomial time approximation algorithm with worst-case ratio of 5/3.