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This article is inspired by human's memory and recognition process to improve neural architecture search (NAS), which has shown novelty and significance in the design of generative adversarial networks (GANs), but the extremely enormous time consumption for searching GAN architectures based on reinforcement learning (RL) limits its applicability to a great extent. The main reason behind the challenge is that, the performance evaluation of subnetworks during the search process takes too much time. To solve this problem, we propose a new algorithm, EfficientAutoGAN, in which a graph convolution network (GCN) predictor is introduced to predict the performance of subnetworks instead of formally assessing or evaluating them. Experiments show that EfficientAutoGAN saves nearly half of the search time and at the same time, demonstrates comparable overall network performance to the state-of-the-art algorithm, AutoGAN, in the field of RL-based NAS for GAN.