To reduce fingerprint acquisition cost and improve positioning accuracy in indoor three-dimensional visible light positioning, a method integrating Gaussian process regression (GPR)-based fingerprint reconstruction with grey wolf optimizer optimized kernel extreme learning machine (GWO-KELM) is proposed. GPR estimates RSS residuals from sparse samples to construct a dense reconstructed fingerprint database, and GWO adaptively optimizes the regularization and kernel parameters of KELM for coordinate prediction. In a 5 m × 5 m × 3 m scenario, the number of collected fingerprint points is reduced by 83.98%, while the average positioning error reaches 3.57 cm and 92% of test errors are below 10 cm.