In this paper, we focus on the tasks scheduling problem in UAV swarm network with power constraint on each UAV. To do so, we propose a distributed optimal scheduling algorithm to achieve optimal task allocation for UAVs with limited power constraint. Our algorithm does not require any prior knowledge of each UAV's state. Hence, each UAV can make its own decision on performing the tasks. The design of our algorithm is enabled by the stochastic network optimization and distributed correlated scheduling. We demonstrate the optimum of our algorithm through theoretical analysis and simulations.