We propose and analyze a unipolar generalized frequency division multiplexing (GFDM) modulation scheme with dimming support for visible light communications (VLC). In the proposed method, the dimming level can be controlled at a transmitter using a single parameter that a receiver need not know. In addition, the dimming parameter can be adjusted by the transmitter at any time without affecting the quality of data transmissions. Expressions of the illumination percentage and the bit error rate (BER) are derived taking into account the dimming parameter, and validated through comparisons with simulation results. Using these expressions, it is possible to specify the dimming parameter at the transmitter based on the desired illumination percentage and estimate the corresponding BER for data transmissions. Numerical results indicate that, compared to adjusting the direct current (DC) bias for dimming control, the proposed method provides a wider dimming range subject to a constraint on the BER.