In this work, a resource management algorithm is proposed for an indoor visible light communication (VLC) access network using an orthogonal frequency division multiple access (OFDMA) scheme. With OFDMA, adaptive modulation is adopted to improve the frequency spectrum efficiency of this VLC system. Specifically, the long-term time-averaged optimization problem is transformed into a series of single timeslot online problems via a Lyapunov optimization technique. Then, each user is provided with a separate queue to maintain the random arrival data by a VLC access point, and a subcarrier allocation solution is subsequently presented to maximize the transmission rate. Numerical simulation shows that compared with the best channel state information (BC) algorithm and round robin (RR) algorithm, the proposed algorithm can not only ensure the transmission rate but also greatly improve system stability. In particular, for mean arrival rate B = 7 K b i t s / t i m e s l o t , the system stability by the proposed algorithm improves by about 53.36% and 61.36% in comparison with BC and RR algorithms, respectively. This work will benefit the design and development of indoor OFDMA VLC systems.