This study proposes a two-step estimator based on a multinomial probit model (MNP-TS) to correct sample selection bias arising in multinomial choice models. The conventional multinomial logit-based correction method relies on a correction term based on a single probability index, which may distort estimation when unobserved factors generate asymmetric bias across alternatives. To address this limitation, this study derives multiple correction terms in the form of generalized inverse Mills ratios using bivariate normal integration. Monte Carlo simulation results show that the proposed MNP-TS estimator performs comparably or better in finite samples under asymmetric selection bias. The estimator also demonstrates computational stability as an alternative to full-information maximum likelihood, which may suffer from convergence problems due to the instability of high-dimensional likelihood functions. An empirical analysis of donation amounts using the 2024 Giving Korea data confirms the practical usefulness of the MNP-TS model.