Uncertainty complicates structural health monitoring (SHM) data modelling and forecasting for high-speed rail (HSR) track slab deformation. Standard Gaussian process (GP) assumes a uniform noise throughout the input space. However, this assumption can be unrealistic for HSR SHM data modelling because of its unique heteroscedastic uncertainty induced by dynamic train loading, electromagnetic interference, large temperature variation and daily maintenance of railway track infrastructure. This study firstly develops a novel online SHM system enabled by fiber Bragg grating (FBG) technology to eliminate electromagnetic interference for continuous and long-term monitoring of track slab deformation, with the capacity of temperature self-compensation. To deal with different sources of uncertainty, a heteroscedastic GP approach, Variational Heteroscedastic Gaussian Process (VHGP), is explored for data modelling, estimation of the monitoring data uncertainty level and data forecasting. Results demonstrate that the VHGP framework yields more robust regression results and the estimated confidence level can better depict the heteroscedastic variances of the noise in HSR data. Higher accuracy for both regression and forecasting is gained through VHGP and the position with maximum noise can be forecasted more accurately.