Abstract: This research considers a project scheduling problem with the object of minimizing weighted earliness-tardiness penalty costs, taking into account a deadline for the project and precedence relations among the activities. An exact recursive method has been proposed for solving the basic form of this problem. We present a new depth-first branch and bound algorithm for extended form of the problem, which time value of money is taken into account by discounting the cash flows. The algorithm is extended with two bounding rules in order to reduce the size of the branch and bound tree. Finally, some test problems are solved and computational results are reported.