Abstract: Deep Neural Networks (DNNs) have succeeded remarkably in various computer tasks. However, they remain vulnerable to adversarial attacks, which could lead to severe security risks. In recent years, robust neural architecture search (NAS) has gradually become an emerging direction for designing adversarially robust architectures. However, existing robust NAS methods rely on repeatedly training numerous DNNs to evaluate robustness, which makes the search process extremely expensive. In this paper, we propose a training-free robust NAS method (TRNAS) that significantly reduces search costs. First, we design a zero-cost proxy model (R-Score) that formalizes adversarial robustness evaluation by exploring the theory of DNN's linear activation capability and feature consistency. This proxy only requires initialized weights for evaluation, which avoids expensive adversarial training costs. Secondly, we introduce a multi-objective selection (MOS) strategy to save candidate architectures with robustness and compactness. Experimental results show that TRNAS only requires 0.02 GPU days to find a promising robust architecture in a vast search space including approximately 10$^{20}$ networks.TRNAS surpasses other state-of-the-art robust NAS methods under both white-box and black-box attacks. Finally, we summarize a few meaningful conclusions for designing the robust architecture and promoting the development of robust NAS field.