Visible light communications (VLC) rely on white light emitting diodes (LEDs) to provide communication and illumination simultaneously. Orthogonal frequency division multiplexing (OFDM) enables bit loading in VLC to make the best use of available modulation bandwidth of white LEDs. However, OFDM signals in VLC exhibit high peak-to-average power ratio (PAPR) as in radio frequency (RF) communications. VLC-OFDM differs from RF-OFDM in that the baseband signals are real-valued and there are two PAPRs to be reduced, namely upper PAPR and lower PAPR. Moreover, upper PAPR and lower PAPR are not independently distributed, and are often subject to asymmetric constraints. In this paper, we propose a distortion-based PAPR reduction scheme to minimize the weighted upper PAPR and lower PAPR in VLC-OFDM. The proposed method takes bit loading into consideration that ensures allocating less distortions to subcarriers with more bits loaded (higher order constellations).