An optimal power allocation scheme in energy harvesting based wireless networks was proposed aiming to maximize the effective capacity under the statistical delay-bounded Quality of Service (QoS). In particular, first, the effective capacity maximization problem was formulated for energy harvesting wireless networks. Next, the effective capacity maximization problem was sovled based on convex optimization theory. By analyzing the solution, the facts were obtained that when the QoS constraint is very loose, the optimal power allocation scheme converges to the water filling scheme; meanwhile, when the QoS constraint is very stringent, the optimal power allocation scheme converges to the channel inversion scheme. Then, the developed optimal power allocation scheme was theoretically analyzed by deriving the channel outage probability. Finally, the performance of the optimal power allocation scheme was tested. The experimental results show that the proposed scheme can obtain larger effective capacity than that existing works.