Glioma, one of the most prevalent and aggressive brain tumors, can significantly reduce life expectancy. The potential carried by noninvasive magnetic resonance imaging (MRI) to help physicians diagnose, determine the extent of tumors, plan treatment, and manage disease was significant. However, automatic brain glioma segmentation from MR scanning remains difficult, time-consuming, and computationally intensive. This paper uses a modified version of LinkNet (mLinkNet) based on convolutional neural networks (CNN) to present an automatic method for detecting brain tumor regions in multiclass brain MRI. Three types of deep CNN models were trained: W-mLinkNet, C-mLinkNet, and E-mLinkNet. The multiclass segmentation problem was solved by dividing it into three binary segmentation steps for glioma regions: whole tumor, tumor core, and growing tumor core, and the models were applied sequentially. In addition, we investigated zero-centering and intensity normalization as preprocessing steps to ensure uniform intensity variation in tissues. To demonstrate the effectiveness of the proposed CNN model, a comparative study was conducted using the Brain Tumor Segmentation Challenge 2015 database (BraTS 2015).