We present an efficient algorithm for power allocation and bit loading in multi-user OFDM system. We start with the close-form optimum power solution based on ideal channel coding and allowing negative transmission power. The solution is then revised by removing the subcarrier of negative power from the objective function and power constraints. The result of this procedure is proven to be the optimum power allocation in the continuous space. The continuing power/rate solution is then mapped to the feasible (non-continuous) rate space. Our algorithm is very efficient in computation (O(N)) and the resultant discrete space power/rate vector is very close to the optimum solution (less than 1% difference in the overall data rate).