Brain cancer is one of the deadliest hazards in the world and hence tumor classification became a dominant task in brain tumor diagnosis. There is a wide range of brain tumors, and each tumor exhibits distinct properties like location, shape, size, and texture. Thus, multi-class brain magnetic resonance (MR) image classification became a trivial task. In this article, we have proposed a seven-layer convolutional neural network to address three-class brain MR image classification. We have employed separable convolution to optimize computation time. The proposed separable convolution based neural network model exhibits accuracy of 97.52% on a publicly available dataset consists of 3064 images. The proposed model has analyzed with the help of four key parameters. Our proposed model exhibits superior performance than existing methods in key parameters. Further, our model takes less training time due to sparse network consists of seven layers.