An anisotropic multi-scale edge detection algorithm is proposed. First, the edge strength maps of the input image are obtained by using a set of anisotropic Gaussian filters at given multiple scales. Then, the obtained edge strength maps are jointly used to produce one fused edge strength map that has higher edge resolution and lower edge diffusion effect. Finally, the fused edge strength map is incorporated into the framework of the Canny edge detection algorithm to generate the final result of edge detection. A new multi-scale fusion strategy based on "signal average" is proposed creatively, and the advantages of the new strategy compared with the existing "geometric average" fusion strategy are explained from the perspective of theoretical analysis and numerical experiments. Experimental results show that the proposed algorithm effectively solves the edge spreading problem of anisotropic filter in a single scale by using multi-scale fusion strategy, and can obtain better edge detection effect than the existing algorithms while maintaining robust noise robustness.