Hyperspectral imagery is characterized by high dimensionality and rich information. How to explore the nature of the high dimensional data more precisely and to find the actual distribution of features are the priorities in the research on hyperspectral remote sensing image processing. It is known that edges in imagery contain some important information regarding to the actual distribution of the objects' features, so it is necessary to study the edge extraction methods for hyperspectral image analysis. In this paper, first the mean shift algorithm is adopted to smooth the dimensionality-reduced hyperspectral data. Then edges of hyperspectral image are extracted after a wavelet transform based dimensionality reduction. Finally, two hyperspectral data sets are tested to validate the proposed algorithm.