Open-Set Recognition (OSR) aims to accurately identify known classes while effectively rejecting unknown classes to guarantee reliability. Most existing OSR methods focus on learning in the spatial domain, where subtle texture and global structure are potentially intertwined. Empirical studies have shown that DNNs trained in the original spatial domain are inclined to over-perceive subtle texture. The biased semantic perception could lead to catastrophic over-confidence when predicting both known and unknown classes. To this end, we propose an innovative approach by decomposing the spatial domain to the frequency domain to separately consider global (low-frequency) and subtle (high-frequency) information, named Frequency Shuffling and Enhancement (FreSH). To alleviate the overfitting of subtle texture, we introduce the High-Frequency Shuffling (HFS) strategy that generates diverse high-frequency information and promotes the capture of low-frequency invariance. Moreover, to enhance the perception of global structure, we propose the Low-Frequency Residual (LFR) learning procedure that constructs a composite feature space, integrating low-frequency and original spatial features. Experiments on various benchmarks demonstrate that the proposed FreSH consistently trumps the state-of-the-arts by a considerable margin.