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Functional logistic regression model in which the response variable takes binary values such as 0 and 1 and the predictor consists of random curves is one of the popular analysis tools for investigating the functional relationship between a binary response and functional predictor. Most of the existing methods used to estimate this model are based on the classical dimension reduction techniques such as functional principal component and functional partial least squares. In addition, they use a least-square type estimator to estimate the model parameters. However, both the classical dimension reduction techniques and the least-squares estimator are are sensitive to atypical observations (outliers), which are common in many empirical applications. In case of outliers, the use of such classical approaches may lead to biased estimates for the model parameters and an increased probability of misclassification. In this study, we propose a robust approach to estimate the regression parameters in the functional logistic regression model. In the proposed method, first, the functional predictor is projected onto a finite-dimensional space via a robust functional principal component analysis. Then, the parameters of the logistic regression model constructed using the binary response and the robust principal component scores are estimated via an M-type estimator. Thus, the proposed method is robust to both outliers in the binary response and the functional predictor (called leverage points). The finite-sample performance of the proposed method is evaluated through a series of Monte-Carlo experiments and an empirical data analysis, and the results are compared with existing classical and robust procedures. Our records reveal that the proposed method produces competitive results with the classical methods when no outlier is present in the data. On the other hand, it produces improved parameter estimate and classification results than the classical methods when the data are contaminated by atypical observations. In addition, our results show that the proposed method produces similar or even better inference for the functional logistic regression model than the existing robust approaches with significantly less computing time.