High resolution range profile (HRRP) classification is an important method for radar complex target classification. Since standard one-against-one hypersphere support vector machine (SVM) has the defects of large computation, long training time for its k(k-1) sub-classifiers, and, decision bland area, it is not fit for HRRP target recognition. In order to reduce the number of classifiers in the one-against-one multi-class, a new one-dimensional membership function based on geometry feature named "reciprocal symmetry" has been defined, and the corresponding fuzzy hypersphere SVM has been given. This new method only needs k(k-1) /2 sub-classifiers, it not only improves the training speed, but also clears away the decision bland area. The HRRP real data experimental results show that this algorithm has better HRRP classification performance.