In this paper, threshold function denoising algorithm and wavelet neural network edge detection algorithm are combined to apply to image edge detection. Firstly, an improved threshold function is constructed in this paper, compared with the traditional soft and hard threshold functions and some existing improved threshold functions, the improved threshold function is adjustable and differentiable everywhere. It approximates the soft threshold function and the image at the threshold point is smoother. It can retain more true information and have an obvious effect in image de-noising. Finally, this paper presents wavelet neural network edge detection algorithm. Selecting the modulation Gaussian function wavelet as its excitation function, which is applied to extract the edge of the image after threshold de-noising. Thus, a new edge detection algorithm is proposed, which combines threshold function de-noising algorithm and wavelet neural network edge detection algorithm. The simulation results show that the edges detected by the new algorithm are clearer, contain less noise, and the continuity and accuracy are also improved.