Branch and bound (BnB) approach, a new algorithm for solving resource allocation in multiuser OFDM system is introduced. It is used in Rate Adaptive allocation. With the classic Genetic Algorithm, the calculation accuracy has been improved, but the complexity is higher. On the other hand, through the branches, bound and cut branches, when used branch and bound algorithm, the complexity is reduced obviously. Simulation results show that it is similar to Genetic Algorithm on the performance, lower complexity than GA, better than Linear Algorithm on the performance.