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In this paper, we propose a Hartley-domain direct-detection faster-than-Nyquist (HD-DD-FTN) algorithm for asymmetrically clipped optical single-carrier frequency-division multiplexing (ACO-SCFDM) in optical-wireless communications (OWC). The HD-DD-FTN algorithm includes modified Hartley-domain equalization (HDE) and maximum likelihood sequence detection, which can simultaneously compensate serious high-frequency distortion and eliminate enhanced in-band noise for the bandwidth-limited OWC. Modified HDE can be implemented by real-valued operations, which is appropriate for dealing with real-valued signals. The simulation results show that ACO-SCFDM system using the HD-DD-FTN algorithm is more robust to inter-symbol interference than that using conventional HDE algorithm. Therefore, the bit error rate performance of the ACO-SCFDM system using HD-DD-FTN algorithm is better than that using the conventional HDE algorithm. In conclusion, the ACO-SCFDM system using the HD-DD-FTN algorithm shows great potential for bandwidth-limited OWC.