In order to satisfy the limitation of interference temperature and total transmission power and to maximizeusers' transmission rate,an optimal power allocation algorithm adaptive to uplink cognitive radio OFDM ( OrthogonalFrequency Division Multiplexing) system is proposed. In this algorithm,first,the zero-setting iterative waterfillingalgorithm under the constraints of total power of the cognitive user is applied to the power allocation. Then,the subcarrier power exceeding the interference power limit is set as the new interference power limit. Finally,theresidual power is allocated to the residual subcarriers by the iterative water-filling algorithm until the optimal powerallocation is achieved. Both the mathematical derivation and the simulation results prove that its proposed algorithmis optimal,and that its computation amount reduces by over 50%,as compared with the gradient method even atthe highest iterative times.