This paper addresses a parallel machine scheduling problem (PMSP) with release dates to minimize sum of completion time. This problem presents numerous potential applications in real life. An efficient exact branch and bound method is developed using theoretical properties. By allowing job splitting or by relaxing release date constraints, a polynomial lower bounding scheme is proposed. The method was tested on more than 2000 randomly generated medium-sized instances. We have solved medium-sized instances in a reasonable amount of time. Our method is the first attempt to solve exactly the considered problem. It opens an interesting way in PMSP with sum of completion time criterion.