The purpose of trademark retrieval is to ensure that new trademarks do not repeat any images of the vast number stored in the trademark registration system. This paper regards the contour of a trademark as a geometric object and represents it precisely in terms of mathematical expressions by employing an orthogonal complete function system, V-system, as a mathematical tool. The boundary feature vector, which captures the overall features of the trademark, is calculated in the frequency domain first. Next, two region feature vectors describing the local characteristics are created by dividing the trademark image into small blocks and considering the distributions of its pixels. Finally, a new trademark retrieval algorithm is achieved by utilizing the weighted Euclidean distance between boundary and region feature vectors. The study conducts different kinds of experiments and adopts several of the evaluation criterions to evaluate the performance of the proposed algorithm. Compared with the methods of classical Fourier descriptor, Zernike moments, Hu invariant moment and combination of Fourier descriptor and Zernike moments, the proposed algorithm has obvious advantages.