Free-space optical communication is emerging as a low-power, low-cost, and high data rate alternative to radio-frequency communication in short- to medium-range applications. However, it requires a close-to-line-of-sight link between the transmitter and the receiver. This paper proposes a robust H∞ control law for free-space optical (FSO) beam pointing error systems under controlled weak turbulence conditions. The objective is to maintain the transmitter–receiver line, which means the center of the optical beam as close as possible to the center of the receiving aperture within a prescribed disturbance attenuation level. First, we derive an augmented nonlinear discrete-time model for pointing error loss due to misalignment caused by weak atmospheric turbulence. We then investigate the H∞-norm optimization problem that guarantees the closed-loop pointing error is stable and ensures the prescribed weak disturbance attenuation. Furthermore, we evaluate the closed-loop outage probability error and bit error rate (BER) that quantify the free-space optical communication performance in fading channels. Finally, the paper concludes with a numerical simulation of the proposed approach to the FSO link’s error performance.