Backdoor attacks against neural networks have been intensively investigated, where the adversary compromises the integrity of the victim model, causing it to make wrong predictions for inference samples containing a specific trigger. To make the trigger more imperceptible and human-unnoticeable, a variety of stealthy backdoor attacks have been proposed, some works employ imperceptible perturbations as the backdoor triggers, which restrict the pixel differences of the triggered image and clean image. Some works use special image styles (e.g., reflection, Instagram filter) as the backdoor triggers. However, these attacks sacrifice the robustness, and can be easily defeated by common preprocessing-based defenses. This paper presents a novel color backdoor attack, which can exhibit robustness and stealthiness at the same time. The key insight of our attack is to apply a uniform color space shift for all pixels as the trigger. This global feature is robust to image transformation operations and the triggered samples maintain natural-looking. To find the optimal trigger, we first define naturalness restrictions through the metrics of PSNR, SSIM and LPIPS. Then we employ the Particle Swarm Optimization (PSO) algorithm to search for the optimal trigger that can achieve high attack effectiveness and robustness while satisfying the restrictions. Extensive experiments demonstrate the superiority of PSO and the robustness of color backdoor against different mainstream backdoor defenses.