Optical orthogonal frequency division multiplexing （OFDM） with index modulation has the advantage of high spectral efficiency （SE）； however， the error performance is not optimal. In this paper， a scheme of asymmetrically clipped optical OFDM with generalized index modulation （ACO-OFDM-GIM） is proposed. In this scheme， the number of active subcarriers in each sub-block can be one or more， and these subcarriers extend the frequency domain modulation. Furthermore， a subcarrier allocation algorithm is adopted to eliminate the correlation between adjacent subcarriers. In this way， a better error performance may be achieved. Taking asymmetrically clipped O-OFDM-GIM （ACO-OFDM-GIM） as an example， the modulation mapping principle of O-OFDM-GIM has been introduced in detail. In addition， the asymptotic bit error probability of the ACO-OFDM-GIM scheme for the turbulence channel is derived and the correctness is verified via simulation. Furthermore， the performance of the ACO-OFDM-GIM system is compared with that of ACO-OFDM and ACO-OFDM-IM systems. The results showed that the transmission rate and the error performance of the ACO-OFDM-GIM scheme are improved compared with the ACO-OFDM-IM and ACO-OFDM schemes. When the SE is indifferent， the error performance of the proposed scheme is greater than ACO-OFDM and ACO-OFDM-IM systems at a large signal noise ratio （SNR）. When the bit error rate is 1×10^-4， the SNR of （4，［1，2］） ACO-OFDM-GIM scheme outperforms that of （4，2） ACO-OFDM-IM and ACO-OFDM schemes nearly 2.5 dB and 4.5 dB， under a strong turbulence channel， respectively. Therefore， the ACO-OFDM-GIM scheme is expected to effectively improve the transmission rate of atmospheric laser communication in the future.