Class-imbalanced and high-dimensional data pose significant challenges in machine learning, often leading to learning models that underperform on minority classes and struggle with the curse of dimensionality, respectively, and these two issues are inherently interconnected. This paper simultaneously addresses both class imbalance and high dimensionality through a multi-task multi-objective feature selection method. To be specific, the proposed method establishes two related yet distinct feature selection problem formulations for a given task, each focusing on different aspects of overall and minority classification performance. By selecting important features from the original imbalanced data set, the proposed method avoids the need to artificially equalize class distribution during training. Additionally, the cross-task genetic transfer operator enables the reuse of valuable feature subsets evolved from separate searches, thereby improving both minority class accuracy and overall model performance. Experimental results on 17 class-imbalanced data sets show that the proposed method achieves better results in terms of overall classification performance and minority class accuracy than the compared state-of-the-art methods, particularly on the high-dimensional data sets.