An efficient supervised orthogonal nonlinear dimensionality reduction algorithm, namely orthogonal margin maximization projection (OMMP), is presented for gait recognition in this paper. Taking the local neighborhood geometry structure and class information into account, the proposed algorithm aims to find a projecting matrix by maximizing the local neighborhood margin between the different classes and preserving the local geometry structure of the data. After projecting, the data points in the same class are pulled as close as possible, while the data points in different classes are pushed as far as possible. The highlights of OMMP include (1) takes both of the local information and class information of the data into account; (2) considers the effect of the noisy points and outliers; (3) it is supervised and orthogonal; and (4) its physical meaning is very clear. The experimental results on a public gait database show the effectiveness of the proposed method.