An optical attocell network is proposed as an indoor small-cell cellular network based on visible light communication (VLC). In this paper, the downlink performance of optical attocell networks is comprehensively analyzed. In particular, signal-to-interference-plus-noise ratio (SINR), outage probability and the resulting achievable cell data rates of optical attocell networks with optical orthogonal frequency division multiplexing (O-OFDM) are analyzed. With different lighting network designs, the cell deployments of optical attocell networks may vary considerably. Hence, attocell networks with different cell deployments are considered and compared. The results show that the hexagonal (HEX) and Poisson Point Process (PPP) random cell deployments represents the best and the worst case performance of practical optical attocell deployments, respectively. In addition, the performance of optical attocell networks is compared with that achieved by other radio frequency (RF) small-cell networks. The results show that a well-designed optical attocell network can perform better than the state-of-the-art femtocell network or millimeter-wave (mmWave) system in terms of indoor area data rate (data rate per unit area).