Layered or hybrid optical orthogonal frequency division multiplexing (OFDM) has been proposed for use in optical communications due to its excellent spectral and power efficiencies, especially in visible light communications (VLC). However, most of the current works concentrate on transmitter and receiver design as well as the quality of service in communication networks. In this paper, we propose a spectrum-efficient dimmable triple-layer hybrid optical OFDM (DTH-OFDM) scheme to tackle the illumination requirements, considering different practical indoor VLC scenarios from low illumination to high illumination intensities. In the proposed DTH-OFDM scheme, the required dimming level is achieved by jointly adjusting the dimming factors and direct current bias. We investigate the comprehensive performance analysis of the proposed DTH-OFDM in detail, including probability density function, bit error rate (BER), spectral and energy efficiencies. In addition, a joint dimming control and optimal power allocation problem for DTH-OFDM is formulated and solved using convex optimization under the constraints of light emitting diode (LED) nonlinearity, dimming target and communications reliability. Numerical results show that, the proposed DTH-OFDM can offer continuous and arbitrary dimming target with higher spectral efficiency and lower BER compared with its counterparts, as well as an enhanced tolerance to the LED nonlinearity.