Graph neural networks (GNNs) have demonstrated significant success in various applications, such as node classification, link prediction, and graph classification. Active learning for GNNs aims to query the valuable samples from the unlabeled data for annotation to maximize the GNNs' performance at a lower cost. However, most existing algorithms for reinforced active learning in GNNs may lead to a highly imbalanced class distribution, especially in highly skewed class scenarios. GNNs trained with class-imbalanced labeled data are susceptible to bias toward majority classes, and the lower performance of minority classes may lead to a decline in overall performance. To tackle this issue, we propose a novel class-balanced and reinforced active learning framework for GNNs, namely, GCBR. It learns an optimal policy to acquire class-balanced and informative nodes for annotation, maximizing the performance of GNNs trained with selected labeled nodes. GCBR designs class-balance-aware states, as well as a reward function that achieves trade-off between model performance and class balance. The reinforcement learning algorithm Advantage Actor-Critic (A2C) is employed to learn an optimal policy stably and efficiently. We further upgrade GCBR to GCBR++ by introducing a punishment mechanism to obtain a more class-balanced labeled set. Extensive experiments on multiple datasets demonstrate the effectiveness of the proposed approaches, achieving superior performance over state-of-the-art baselines.