The accumulation of large amounts of historical data has led to the wide application of ensemble learning over the past few decades, but the balance between the individual accuracy of base classifiers (BCs) and the diversity among these BCs is rarely considered in the construction of ensemble models. Since such a balance is crucial to the success of ensemble models, this paper proposes a Genetic Algorithm-based sequential instance selection framework to address this research gap. The novelties of the proposed framework include: transforming the balance between the individual accuracy of BCs and the diversity among BCs into a general combinatorial optimization model and designing a Genetic Algorithm-based evolutionary instance selection method to solve this model. The proposed framework not only overcomes the inherent limitations of the Genetic Algorithm in some high-dimensional tasks but also provides an explicit and automatic way to balance the accuracy and diversity by searching appropriate training data subsets for different component BCs. Based on obtained training data subsets, the component BCs of the ensemble model are generated sequentially, and their predictions are further combined with the weighted majority voting rule. Using 30 real datasets collected from various practical applications, such as medicine, business, and industry, the effectiveness of the proposed framework in constructing powerful ensemble models is examined and compared with six benchmark ensemble learning methods. In addition, the capability of the proposed framework to improve convergence performances is also examined by the comparison with the traditional Genetic Algorithm.