Many existing neural architecture search (NAS) solutions rely on downstream training for architecture evaluation, which takes enormous computations. Considering that these computations bring a large carbon footprint, this paper aims to explore a green (namely environmental-friendly) NAS solution that evaluates architectures without training. Intuitively, gradients, induced by the architecture itself, directly decide the convergence and generalization results. It motivates us to propose the gradient kernel hypothesis that gradients can be used as a coarse-grained proxy of downstream training to evaluate random-initialized networks. To support the hypothesis, we conduct a theoretical analysis and find a practical gradient kernel that has good correlations with training loss and validation performance. According to this hypothesis, we propose a new kernel based architecture search approach KNAS. Experiments show that KNAS achieves competitive results with orders of magnitude faster than “train-then-test” paradigms on image classification tasks. Furthermore, the extremely low search cost enables its wide applications. The searched network also outperforms strong baseline RoBERTA-large on two text classification tasks.