The research on developing CNN-based fully-automated Brain-Tumor-Segmentation systems has been progressed rapidly. For the systems to be applicable in practice, a good The research on developing CNN-based fully-automated Brain-Tumor-Segmentation systems has been progressed rapidly. For the systems to be applicable in practice, a good processing quality and reliability are the must. Moreover, for wide applications of such systems, a minimization of computation complexity is desirable, which can also result in a minimization of randomness in computation and, consequently, a better performance consistency. To this end, the CNN in the proposed system has a unique structure with 2 distinguished characters. Firstly, the three paths of its feature extraction block are designed to extract, from the multi-modality input, comprehensive feature information of mono-modality, paired-modality and cross-modality data, respectively. Also, it has a particular three-branch classification block to identify the pixels of 4 classes. Each branch is trained separately so that the parameters are updated specifically with the corresponding ground truth data of a target tumor areas. The convolution layers of the system are custom-designed with specific purposes, resulting in a very simple config of 61,843 parameters in total. The proposed system is tested extensively with BraTS2018 and BraTS2019 datasets. The mean Dice scores, obtained from the ten experiments on BraTS2018 validation samples, are 0.787+0.003, 0.886+0.002, 0.801+0.007, for enhancing tumor, whole tumor and tumor core, respectively, and 0.751+0.007, 0.885+0.002, 0.776+0.004 on BraTS2019. The test results demonstrate that the proposed system is able to perform high-quality segmentation in a consistent manner. Furthermore, its extremely low computation complexity will facilitate its implementation/application in various environments.