High-precision indoor positioning has been viewed as a crucial challenge for 6G integrated communication and sensing networks, where the visible light-based positioning can provide a cost-efficient solution due to its line-of-sight. However, it is susceptible to high blockage, where the light of light-emitting diode (LED) can be blocked by obstacles and moving objects and then the conventional positioning methods do not perform well. In this paper, we propose a low-complexity machine-learning based visible light positioning (VLP) method in the context of the high-blockage scenario. In the proposed design, we explore the positioning accuracy of various machine-learning algorithms including the K-nearest neighbor (KNN), the extreme learning machine (ELM) and the random forest (RF), based on the channel impulse response. Furthermore, we establish the fingerprint database and vary the weights for these machine learning methods, to achieve a mean square error (MSE) as low as 0.046 m, while achieving precise positioning within 10cm with an 85% probability. We also demonstrate that all three methods can support high-precision indoor positioning through simulation analysis.