Power allocation is investigated for a wireless transceiver pair, in which the transmitter is powered by energy harvesting and some knowledge of the energy arrival process is known. We propose to perform power allocation in two levels. In the upper level, average transmit power is allocated for stages (a stage contains a number of fading blocks). In the lower level, power allocation over fading blocks is performed within each stage, given average transmit power level allocated in the upper level for the stage. Optimal solution to the lower level that aims at ergodic capacity maximization is obtained in semi-closed-form. The upper level aims at maximization of the system throughput over the stages. As the upper-level problem is nonconvex, by using an approximation, we transform the problem into a monotonic optimization problem, which can be solved by existing numerical algorithms. Simulation demonstrates that, compared to an exhaustive search method, our proposed method has significantly less running time, at the cost of a not-significant throughput loss.