In the system of Marr's theory on computer vision, image edge detection plays an important role. Research on the typical problem in computer vision, however, is very difficult because of the complexity and limitation of the available techniques. The main aim of this paper was trying to apply wavelets to image edge detection since wavelet analysis technique is a breakthrough in mathematical tools and methods in recent decade. According to the meteyard of edge detection and consulting the design-aim of optimal edge-filter, this paper discussed the general rules of selecting the mother function of wavelet used in edge detection, then constructed a quadric B-spline wavelet and presented a method of adaptive thresholds edge detection for image based on wavelet transform. The algorithm was validated using computer simulation, and the result was better than that using fixed thresholds.