This paper considers the downlink power allocation in the ultra-dense network. To acquire the maximum sum rate of all the users, we first make the appropriate approximate hypothesis on the interference, and then adopt the Lagrangian Multiplier method and Karush-Kuhn-Tucker condition to obtain the expression of the optimum power allocation. Finally, the iteratively searching water filling ... [Show full abstract] algorithm is used to allocate power for each access node, when the total power is limited. Due to the consideration of the computation complexity of the iteratively searching algorithm, we applied the low-complexity water filling algorithm into the power allocation to reduce the iteration times. The simulation results have shown that the performance of the both two water filling algorithms are close, and can improve the sum rate of the users in the ultra-dense network, and the low-complexity water filling algorithm can converge to the optimum solution more quickly.