Brain tumors pose a complex and urgent challenge in medical diagnostics, requiring precise and timely classification due to their diverse characteristics and potentially life-threatening consequences. While existing deep learning (DL)-based brain tumor classification (BTC) models have shown significant progress, they encounter limitations like restricted depth, vanishing gradient issues, and difficulties in capturing intricate features. To address these challenges, this paper proposes an efficient skip connections-based residual network (ESRNet). leveraging the residual network (ResNet) with skip connections. ESRNet ensures smooth gradient flow during training, mitigating the vanishing gradient problem. Additionally, the ESRNet architecture includes multiple stages with increasing numbers of residual blocks for improved feature learning and pattern recognition. ESRNet utilizes residual blocks from the ResNet architecture, featuring skip connections that enable identity mapping. Through direct addition of the input tensor to the convolutional layer output within each block, skip connections preserve the gradient flow. This mechanism prevents vanishing gradients, ensuring effective information propagation across network layers during training. Furthermore, ESRNet integrates efficient downsampling techniques and stabilizing batch normalization layers, which collectively contribute to its robust and reliable performance. Extensive experimental results reveal that ESRNet significantly outperforms other approaches in terms of accuracy, sensitivity, specificity, F-score, and Kappa statistics, with median values of 99.62%, 99.68%, 99.89%, 99.47%, and 99.42%, respectively. Moreover, the achieved minimum performance metrics, including accuracy (99.34%), sensitivity (99.47%), specificity (99.79%), F-score (99.04%), and Kappa statistics (99.21%), underscore the exceptional effectiveness of ESRNet for BTC. Therefore, the proposed ESRNet showcases exceptional performance and efficiency in BTC, holding the potential to revolutionize clinical diagnosis and treatment planning.