We propose a robust method for outlier detection in functional data analysis. This approach uses the robust Minimum Covariance Determinant estimator to compute the Mahalanobis distance applied to functional principal component scores. The main contribution of this research is the detection of outlier curves using the robust covariance matrix of functional principal components, in contrast to existing methods that use principal components on the discrete dataset. The proposed method is practical because it considers the entire functional form of the data, through their functional principal components, providing a comprehensive analysis that can detect anomalies across the entire functional range. A simulation study compares this approach with existing methods to evaluate their performance, followed by applications to El Niño Sea Surface Temperature data and SCImago Journal Rank data. The results show that the proposed method provides greater accuracy, demonstrating its effectiveness in detecting outlier curves.