This paper presents a technique for structure damage detection based on the wavelet analysis. The main purpose of this paper is to predict the positions of damage based on spatial wavelet analysis. Many damage detection methods require modal properties before and after damage. This method only needs the spatially distributed signals (e.g. the displacements) of the beam after damage. First, spatially distributed signals of the variable-cross-section beam with damage are obtained by finite element method. In this paper, the damaged region is represented as the elements with reduced stiffness. Then the displacements of damaged beam are analyzed by wavelet transformation. It is observed that distributions of the wavelet coefficients can identify the damage position of the variable-cross-section beam by showing a peak at the position of the damage.