This paper presents a novel noise robust edge detector based upon the automatic anisotropic Gaussian kernels (ANGKs), which also addresses the current problem that the seminal Canny edge detector may miss some obvious crossing edge details. Firstly, automatic ANGKs are designed according to the noise suppression, edge resolution and localization precision, which also conciliate the conflict between them. Secondly, reasons why cross-edge points are missing from Canny detector results using isotropic Gaussian kernel are analyzed. Thirdly, the automatic ANGKs are used to smooth image and a revised edge extraction method is used to extract edges. Finally, the aggregate test receiver-operating-characteristic (ROC) curves and Pratt's Figure of Merit (FOM) are used to evaluate the proposed detector against state-of-the-art edge detectors. The experiment results show that the proposed algorithm can obtain better performance for noise-free and noisy images.