Light emitting diodes (LEDs) based visible light communication (VLC) has been considered as a promising technology for indoor high-speed wireless access, due to its unique advantages, such as low cost, license free and high security. To achieve high-speed VLC transmission, carrierless amplitude and phase (CAP) modulation has been utilized for its lower complexity and high spectral efficiency. Moreover, to compensate the linear and nonlinear distortions such as frequency attenuation, sampling time offset, LED nonlinearity etc., series of pre- and post-equalization schemes should be employed in high-speed VLC systems. In this paper, we make an investigation on several advanced pre- and postequalization schemes for high-order CAP modulation based VLC systems. We propose to use a weighted preequalization technique to compensate the LED frequency attenuation. In post-equalization, a hybrid post equalizer is proposed, which consists of a linear equalizer, a Volterra series based nonlinear equalizer, and a decision-directed least mean square (DD-LMS) equalizer. Modified cascaded multi-modulus algorithm (M-CMMA) is employed to update the weights of the linear and the nonlinear equalizer, while DD-LMS can further improve the performance after the preconvergence. Based on high-order CAP modulation and these equalization schemes, we have experimentally demonstrated a 1.35-Gb/s, a 4.5-Gb/s and a 8-Gb/s high-speed indoor VLC transmission systems. The results show the benefit and feasibility of the proposed equalization schemes for high-speed VLC systems.