In this paper, we propose and experimentally demonstrate a high rate-distance product visible light communication (VLC) system based on nonlinearity-adaptive hybrid probabilistic-geometric constellation shaping (NA-HCS) for multi-kilometer free space transmission. A pairwise optimization algorithm is employed within the probabilistic shaping (PS) to achieve NA-HCS for constellation according to the pre-estimated signal-to-noise ratio (SNR) of the long-distance nonlinear channel, which proves its efficacy in channel capacity optimization. Using a modified physical free space optical communication equivalent link, the QAM based on NA-HCS technology can flexibly control the net data rate (NDR) to accommodate different intensities of nonlinear impairment within 1 km transmission channel, consistently outperforming PS-APSK and PS-QAM. Additionally, we also investigate the performance of the NA-HCS technology over longer distances. A maximum rate-distance product of 61.12 Gbit/skm with NDR of 7.64 Gbit/s over 8 km distance has been successfully demonstrated using the NA-HCS-64QAM system with a 530 nm laser diode. The perspective of this scheme is directed toward future long-haul free space optical communication networks.