The evolutionary paradigm has been successfully applied to neural network search(NAS) in recent years. Due to the vast search complexity of the global space, current research mainly seeks to repeatedly stack partial architectures to build the entire model or to seek the entire model based on manually designed benchmark modules. The above two methods are attempts to reduce the search difficulty by narrowing the search space. To efficiently search network architecture in the global space, this paper proposes another solution, namely a computationally efficient neural architecture evolutionary search framework based on network growth (G-EvoNAS). The complete network is obtained by gradually deepening different Blocks. The process begins from a shallow network, grows and evolves, and gradually deepens into a complete network, reducing the search complexity in the global space. Then, to improve the ranking accuracy of the network, we reduce the weight coupling of each network in the SuperNet by pruning the SuperNet according to elite groups at different growth stages. The G-EvoNAS is tested on three commonly used image classification datasets, CIFAR10, CIFAR100, and ImageNet, and compared with various state-of-the-art algorithms, including hand-designed networks and NAS networks. Experimental results demonstrate that G-EvoNAS can find a neural network architecture comparable to state-of-the-art designs in 0.2 GPU days.