Brain tumor localization and segmentation from magnetic resonance imaging (MRI) are hard and important tasks for several applications in the field of medical analysis. As each brain imaging modality gives unique and key details related to each part of the tumor, many recent approaches used four modalities T1, T1c, T2, and FLAIR. Although many of them obtained a promising segmentation result on the BRATS 2018 dataset, they suffer from a complex structure that needs more time to train and test. So, in this paper, to obtain a flexible and effective brain tumor segmentation system, first, we propose a preprocessing approach to work only on a small part of the image rather than the whole part of the image. This method leads to a decrease in computing time and overcomes the overfitting problems in a Cascade Deep Learning model. In the second step, as we are dealing with a smaller part of brain images in each slice, a simple and efficient Cascade Convolutional Neural Network (C-ConvNet/C-CNN) is proposed. This C-CNN model mines both local and global features in two different routes. Also, to improve the brain tumor segmentation accuracy compared with the state-of-the-art models, a novel Distance-Wise Attention (DWA) mechanism is introduced. The DWA mechanism considers the effect of the center location of the tumor and the brain inside the model. Comprehensive experiments are conducted on the BRATS 2018 dataset and show that the proposed model obtains competitive results: the proposed method achieves a mean whole tumor, enhancing tumor, and tumor core dice scores of 0.9203, 0.9113 and 0.8726 respectively. Other quantitative and qualitative assessments are presented and discussed.