Tumor segmentation is a valuable tool for gaining insights into tumors and improving treatment outcomes. Manual segmentation is crucial but time-consuming. Deep learning methods have emerged as key players in automating brain tumor segmentation. In this paper, we propose an efficient modified U-Net architecture, called EMU-Net, which is applied to the BraTS 2020 dataset. Our approach is organized into two distinct phases: classification and segmentation. In this study, our proposed approach encompasses the utilization of the gray-level co-occurrence matrix (GLCM) as the feature extraction algorithm, convolutional neural networks (CNNs) as the classification algorithm, and the chi-square method for feature selection. Through simulation results, the chi-square method for feature selection successfully identifies and selects four GLCM features. By utilizing the modified U-Net architecture, we achieve precise segmentation of tumor images into three distinct regions: the whole tumor (WT), tumor core (TC), and enhanced tumor (ET). The proposed method consists of two important elements: an encoder component responsible for down-sampling and a decoder component responsible for up-sampling. These components are based on a modified U-Net architecture and are connected by a bridge section. Our proposed CNN architecture achieves superior classification accuracy compared to existing methods, reaching up to 99.65%. Additionally, our suggested technique yields impressive Dice scores of 0.8927, 0.9405, and 0.8487 for the tumor core, whole tumor, and enhanced tumor, respectively. Ultimately, the method presented demonstrates a higher level of trustworthiness and accuracy compared to existing methods. The promising accuracy of the EMU-Net study encourages further testing and evaluation in terms of extrapolation and generalization.