This study investigates the nonlinear impact of various modes of transportation (air, road, railway, and maritime) on the number of foreign visitors to China originating from major source countries. Our nonlinear tourism demand equations are determined through the Markov-switching regression (MSR) model, thereby, capturing the possible structural changes in Chinese tourism demand. Due to many variables and the limitations from the small number of observations confronted in this empirical study, we may face multicollinearity and endogeneity bias. Therefore, we introduce the two penalized maximum likelihoods, namely Ridge and Lasso, to estimate the high dimensional parameters in the MSR model. This investigation found the structural changes in all tourist arrival series with significant coefficient shifts in transportation variables. We observe that the coefficients are relatively more significant in regime 1 (low tourist arrival regime). The coefficients in regime 1 are all positive (except railway length in operation), while the estimated coefficients in regime 2 are positive in fewer numbers and weak. This study shows that, in the process of transportation, development and changing inbound tourism demand from ten countries, some variables with the originally strong positive effect will have a weak positive effect when tourist arrivals are classified in the high tourist arrival regime.