Considering that metro network expansion brings us with more alternative routes, it is attractive to integrate the impacts of routes set and the interdependency among alternative routes on route choice probability into route choice modeling. Therefore, the formulation, estimation and application of a constrained multinomial probit (CMNP) route choice model in the metro network are carried out in this paper. The utility function is formulated as three components: the compensatory component is a function of influencing factors; the non-compensatory component measures the impacts of routes set on utility; following a multivariate normal distribution, the covariance of error component is structured into three parts, representing the correlation among routes, the transfer variance of route, and the unobserved variance respectively. Considering multidimensional integrals of the multivariate normal probability density function, the CMNP model is rewritten as Hierarchical Bayes formula and M-H sampling algorithm based Monte Carlo Markov Chain approach is constructed to estimate all parameters. Based on Guangzhou Metro data, reliable estimation results are gained. Furthermore, the proposed CMNP model also shows a good forecasting performance for the route choice probabilities calculation and a good application performance for transfer flow volume prediction.