Abstract This paper proposes a new and efficient framework to deal with the classification of data streams when exhibiting feature drifts. The first building block of the framework is a dynamic multi-objective evolutionary algorithm called Dynamic Filter-Based Feature Selection (DFBFS) algorithm, which handles feature drifts by continuously selecting the optimal set during the stream processing. Moreover, a new feature drift detection method is proposed to incorporate with the DFBFS algorithm. In the proposed framework, the Artificial Neural Network (ANN) is utilized to classify the data streams by only focusing on the features selected by the DFBFS algorithm. The empirical study for evaluating the framework performance utilizes four different dataset generators by varying environmental parameters in terms of change severity and change frequency. Experimental evaluation validates our framework, as it significantly outperforms reference algorithms in terms of classification accuracy and the ability of fast recovery after the occurrence of feature drifts on the evaluated datasets.