Image corners have been widely used in various computer vision tasks. Current multi-scale analysis based corner detectors do not make full use of the multi-scale and multi-directional structural information. This degrades their detection accuracy and capability of refining corners. In this work, an improved shearlet transform with a flexible number of directions and a reasonable support is proposed to extract accurate multi-scale and multi-directional structural information from images. To make full use of the structural information from the improved shearlets, a novel multi-directional structure tensor is constructed for corner detection, and a multi-scale corner measurement function is proposed to remove false candidate corners. Experimental results demonstrate that the proposed corner detector performs better than existing corner and interest point detectors in terms of detection accuracy, localization accuracy, and robustness to affine transformations, illumination changes, noise, viewpoint changes, etc. It has a great potential for extension as a descriptor and for applications in computer vision tasks.