In this paper, a novel target recognition method, namely orthogonal maximum margin projection subspace (OMMPS), is proposed for radar target recognition using high-resolution range profile (HRRP). The core of OMMPS is to maximize the between-class margin by increasing the between-class scatter distance and reducing the within-class scatter distance simultaneously. By introducing the nonlinear mapping function, we also derive the kernel version of OMMPS, namely orthogonal kernel maximum margin projection subspace (OKMMPS). Compared with maximum margin criterion (MMC) method, OMMPS are optimal in meaning of maximum margin due that the coordinate axes of OMMPS are obtained sequentially by solving the constrained optimization problem, thus improves the recognition performance. In addition, the number of efficient features for OMMPS is not limited by the number of pattern classes, and the appropriate features can still be obtained for separating the classes, even in high-dimensional space with only a few classes. Moreover, the coordinate axes of OMMPS are mutually orthogonal, and the features extracted by OMMPS reduce the redundancy. The extensive experimental results show that the proposed method has better recognition performance than the other methods such as MMC and LDA.