High-altitude airborne platforms interconnected by free-space optical communications (FSOCs) have recently emerged as a promising solution for establishing wireless networks for rural and remote areas. The performance of FSOC system is severely degraded by the angle-of-arrival (AoA) fluctuation and pointing error. The precise alignment between the optical transmitter and receiver can be achieved by using the pointing, acquisition, and tracking (PAT), but it should work within the tight constraints of airborne platforms on size, weight, and power. It is also highly desirable that the PAT operates rapidly (e.g., without iteration for optimization) since the airborne platforms can be on the fast move. We propose a rapid and computation power-efficient adaptive beam control technique, where the beam sizes are adjusted without iterations at both the transmitter and receiver using nonmechanical variable-focus lenses, to mitigate the deleterious effects of AoA fluctuation and pointing error simultaneously. For this purpose, we provide the closed-form expressions about the optimum beam sizes at the transmitter and receiver for the outage probability. We carry out Monte Carlo simulations to validate the accuracy of our theoretical derivations. We show that the airborne FSOC system using the adaptive beam control technique outperforms the system having fixed beam sizes over wide ranges of AoA fluctuation and pointing error.