The purpose of the paper is to classify the Leukemia images. In this paper, we proposed a commutative model of a convolutional neural network for Leukemia image classification. We employ commutative hypercomplex modeling A[+1, -1] and A[-1, +1] to build the new model. We hire an augmentation model to enrich the image data sets for the training sets through rotation, zooming, and flipping. We evaluated our proposed method using acute lymphoblastic leukemia image database type 2 (ALL-IDB2). The results show that our proposed method has delivered the best average accuracy at 96.43% for A[+1,-1] and 97.05 for A[-1,+1]. We have measured and found maximum accuracy at 100% for A[+1,-1] and A[-1,+1]. Comparison results show that our proposed method outperformed Knearest neighbor, support vector machine-radial basis function, support vector machine-linear, support vector machinepolynomial, naïve bayes gaussian, naïve bayes complement, decision tree, and colour hybrid modelling.