The research on developing CNN-based fully-automated brain-tumor-segmentation systems has been progressing rapidly. For the systems to be applicable in practice, a good processing quality and reliability are necessary. Moreover, as the parameters in a CNN are determined by training, based on statistical losses in training epochs, more parameters may cause more randomness in the process and a minimization of the number of parameters is required to achieve a good reproducibility of the results. 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 distinguish pixels in each of the 3 intra-tumoral classes from the background. Each branch is trained separately so that the parameters are updated specifically with the corresponding ground truth data of target tumor areas. The convolutional 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 has been tested extensively with BraTS2019 and BraTS2018 datasets. The mean Dice scores, obtained from the ten experiments on BraTS2019 validation samples, are 0.751 +/- 0.007, 0.885 +/- 0.002, 0.776 +/- 0.004, for enhancing tumor, whole tumor and tumor core, respectively. The test results demonstrate that the proposed system is able to reproduce a high -quality segmentation result quite consistently. Furthermore, its extremely low computation complexity will facilitate its implementation/application in various environments.