This letter describes a theoretical framework for power distribution to minimize an energy outage (EO) of off-grid base stations (BSs) powered by renewable energy sources and battery storage without direct support of an electrical grid. Here, EOs may occur when off-grid BSs cannot meet the power demand. Thus, considering the transmission power of the BS according to the traffic load and battery capacity, we represent an EO probability model. Using this model, we propose an energy outage-aware power distribution scheme (EO-PDS) for off-grid BSs. The convex optimization problem for minimizing the EO in off-grid BSs is formulated and solved. Numerical results reveal that the proposed scheme significantly reduces the EO probability compared with other existing schemes and has an acceptable convergence time.