Brain tumor image classification is one of the predominant tasks of brain image processing. The three-class brain tumor classification becomes a trivial task for researchers as each tumor exhibit distinct characteristics. Existing classification models use deep neural networks and suffer from high computational cost. We have proposed an eight-layer average-pooling convolutional neural network to address three-class brain tumor classification. The proposed model uses three convolution blocks along with a dense layer and a softmax layer. We have utilized N-adam optimizer with a sparse-categorical cross-entropy loss function to improve the learning rate. The proposed model has been evaluated using a dataset consists of 3064 brain tumor magnetic resonance images. The proposed model outperforms state-of-the-art models with 97.42% accuracy and takes lesser computation time than its competitive models.