It is much more complex and difficult for edge detection of noise image compared to edge detection of normal image，the analysis and study of edge detection of noise image has universal significance and practical value. Wavelet transform possesses good time-frequency localization characteristic and multi-scale analytical ability, mathematical morphology is a new subject based on set theory, which is very suitable for analyzing and describing geometrical feature of signal. Combining the advantages of wavelet transform and mathematical morphology, the paper proposes an edge detection algorithm, which mainly focused on noise image. For edge detection based on mathematical morphology, constructs an anti-noise operator of edge detection by improving existing operators and employs different direction linear structure elements; edge detection based on mathematical morphology can reserve details of edge effectively, ensure the continuity and integrity of edge detected. Experimental results show the proposed algorithm can suppress the interference of different density and different types of noise more effectively in comparison with several classical edge detection algorithm, thus improving the detection accuracy and robustness for different images.