A novel machine learning algorithm named pruning support vector data description (PSVDD) is developed to classify the FFT-magnitude feature of complex high-resolution range profile (HRRP), motivated by the problem of radar automatic target recognition (RATR). The PSVDD algorithm not only inherits the advantage of LSSVM model, which owns low computational complexity with linear equality constraints so that it is convenient to prune the boundary of SVDD dynamically and quickly, but also overcomes the shortcoming of poor handing capacity of variable outliers in SVDD. Besides, similar to the LSSVM, the proposed method is aimed to find the distribution information within classes by least square before classification, and then this information is applied into the PSVDD, thus there will be a remarkable improvement in classification accuracy and recognition performance. Numerical experiments based on HRRPs of four aircrafts can demonstrate the feasibility and superiority of the proposed algorithm.