An illumination-independent wavelet scale multiplication edge detection method is proposed to detect edges from the non-uniform weak illumination image. Based on the illumination-reflected image formation model and CCD camera imaging formula, the image wavelet transform formula is deduced. The wavelet module coefficients of the background pixel, noise, edges are observed and analyzed in the local region, and the illumination-independent wavelet edge detection algorithm is worked out. To enhance edge pixels and reduce noise, an improved wavelet scale multiplication edge detection algorithm is applied to orient edges accurately. Through utilizing edge pixels' characteristics after wavelet transform, the single-pixel edges are taken out of the image. In the end, the edge detection experiments for synthetic and real non-uniform weak illumination images were conducted, and its performance is analyzed and compared with other two edge detection methods qualitatively and quantitatively. The experimental result proves it correct and effective when used in the non-uniform gray and low contrast images to detect edges.