A cooperative orthogonal frequency division multiplexing (OFDM) system with a source and a non-regenerative relay transmitting according to Alamouti’s STBC is considered. The capacity of the system is analyzed and the analytical expression is presented. To improve the capacity of the individual power constrained system, a power allocation algorithm named as the Stepwise Iterative Power Allocation Algorithm (SIPAA) is proposed. The basic principle of SIPAA is that the water filling power allocation is implemented stepwise for both the source and the relay within iterations. To reduce the complexity of SIPAA, the object function is linearly processed before the water-filling power allocation, and the power vector is also linearly processed after the water-filling power allocation. It is confirmed by the simulation results that a significant system capacity improvement can be achieved by the proposed algorithm, compared with conventional equal power allocation algorithm. Moreover, the power allocation can be completed within a few iterations.