The performance of convolutional neural networks (CNNs) highly relies on their architectures. In order to design a CNN with promising performance, extensive expertise in both CNNs and the investigated problem domain is required, which is not necessarily available to every interested user. To address this problem, we propose to automatically evolve CNN architectures by using a genetic algorithm (GA) based on ResNet and DenseNet blocks. The proposed algorithm is completely automatic in designing CNN architectures. In particular, neither preprocessing before it starts nor postprocessing in terms of CNNs is needed. Furthermore, the proposed algorithm does not require users with domain knowledge on CNNs, the investigated problem, or even GAs. The proposed algorithm is evaluated on the CIFAR10 and CIFAR100 benchmark data sets against 18 state-of-the-art peer competitors. Experimental results show that the proposed algorithm outperforms the state-of-the-art CNNs hand-crafted and the CNNs designed by automatic peer competitors in terms of the classification performance and achieves a competitive classification accuracy against semiautomatic peer competitors. In addition, the proposed algorithm consumes much less computational resource than most peer competitors in finding the best CNN architectures.