The multiprocessor task graph scheduling problem has been extensively studied as academic optimization problem which occurs in optimizing the execution time of parallel algorithm with parallel computer. The problem is already being known as one of the NPhard problems. There are many good approaches made with many optimizing algorithm to find out the optimum solution for this problem with less computational time. One of them is branch and bound algorithm. In this paper, we propose a branch and bound algorithm for the multiprocessor scheduling problem. We investigate the algorithm by comparing two different lower bounds with their computational costs and the size of the pruned tree. Several experiments are made with small set of problems and results are compared in different sections.