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This paper investigates the cross-correlation characteristics of large-scale parameters (LSPs) and small-scale fading (SSF) for high-speed railway (HSR) multi-link propagation scenarios, based on realistic measurements conducted on Beijing to Tian-jin HSR line in China. A long-term evolu-tion-based channel sounding system is utilized in the measurements to obtain the channel data. By applying a proposed time-delay based dynamic partition method, multi-link channel impulse responses are extracted from the raw channel data. Then, the statistical results of LSPs, including shadow fading, K-factor, and root-mean-square delay spread are derived and the cross-correlation coefficients of these LPSs are calculated. Moreover, the SSF spatial correlation and cross-correlation of SSF are analyzed. These results can be used to exploit multi-link channel model and to optimize the next-generation HSR communication system.