The convolutional neural network (CNN), one of the deep learning models, has demonstrated outstanding performance in a variety of computer vision tasks. However, as the network architectures become deeper and more complex, designing CNN architectures requires more expert knowledge and trial and error. In this article, we attempt to automatically construct high-performing CNN architectures for a given task. Our method uses Cartesian genetic programming (CGP) to encode the CNN architectures, adopting highly functional modules such as a convolutional block and tensor concatenation, as the node functions in CGP. The CNN structure and connectivity, represented by the CGP, are optimized to maximize accuracy using the evolutionary algorithm. We also introduce simple techniques to accelerate the architecture search: rich initialization and early network training termination. We evaluated our method on the CIFAR-10 and CIFAR-100 datasets, achieving competitive performance with state-of-the-art models. Remarkably, our method can find competitive architectures with a reasonable computational cost compared to other automatic design methods that require considerably more computational time and machine resources.