Texture surface anomaly detection finds widespread applications in industrial settings. However, existing methods often necessitate gathering numerous samples for model training. Moreover, they predominantly operate within a close-set detection framework, limiting their ability to identify anomalies beyond the training dataset. To tackle these challenges, this paper introduces a novel zero-shot texture anomaly detection method named Global-Regularized Neighborhood Regression (GRNR). Unlike conventional approaches, GRNR can detect anomalies on arbitrary textured surfaces without any training data or cost. Drawing from human visual cognition, GRNR derives two intrinsic prior supports directly from the test texture image: local neighborhood priors characterized by coherent similarities and global normality priors featuring typical normal patterns. The fundamental principle of GRNR involves utilizing the two extracted intrinsic support priors for self-reconstructive regression of the query sample. This process employs the transformation facilitated by local neighbor support while being regularized by global normality support, aiming to not only achieve visually consistent reconstruction results but also preserve normality properties. We validate the effectiveness of GRNR across various industrial scenarios using eight benchmark datasets, demonstrating its superior detection performance without the need for training data. Remarkably, our method is applicable for open-set texture defect detection and can even surpass existing vanilla approaches that require extensive training.