The design and performance evaluation of the high-speed railway (HSR) communications are inseparable from the accurate and efficient high-speed channel simulator. The variation on path loss, shadowing and fast fading are the key characteristics of HSR channels. Although finite-state Markov chain (FSMC) channel models have been extensively investigated to describe fading channels, most of the previous channel simulators cannot reflect all the above key characteristics. In this paper, we propose a novel FSMC model based on channel simulator with the path loss, shadowing and fast fading in HSR. The accurate closed-form expression of state transition probabilities between channel states is derived to break the simplified assumption of first-order Markov chain. To validate the accuracy of the new FSMC channel simulator, the comparison analysis between the proposed channel simulator and the actual measurements are provided.