We propose a model-based predictive estimator of the finite population proportion of a misclassified binary response, when information on the auxiliary variable(s) is available for all units in the population. Asymptotic properties of the misclassification-adjusted predictive estimator are also explored. We propose a computationally efficient bootstrap variance estimator that exhibits better performance compared to usual analytical variance estimator. The performance of the proposed estimator is compared with other commonly used design-based estimators through extensive simulation studies. The results are supplemented by an empirical study based on literacy data.