An efficient sieve maximum likelihood estimation procedure for regression models with endogenous regressors using a copula-based approach is proposed. Specifically, the joint distribution of the endogenous regressor and the error term is characterized by a parametric copula function evaluated at the nonparametric marginal distributions. The asymptotic properties of the proposed estimator are derived, including semiparametrically efficient property. Monte Carlo simulations reveal that the proposed method performs well in finite samples comparing to other existing methods. An empirical application is presented to demonstrate the usefulness of the proposed approach.