Feature point matching that incorporates pairwise constraints can be cast as an integer quadratic programming (IQP) problem. Since it is NP-hard, approximate methods are required. The optimal solution for IQP matching problem is discrete, binary, and thus sparse in nature. This motivates us to use sparse model for feature point matching problem. The main advantage of the proposed sparse feature point matching (SPM) method is that it generates sparse solution and thus naturally imposes the discrete mapping constraints approximately in the optimization process. Therefore, it can optimize the IQP matching problem in an approximate discrete domain. In addition, an efficient algorithm can be derived to solve SPM problem. Promising experimental results on both synthetic points sets matching and real-world image feature sets matching tasks show the effectiveness of the proposed feature point matching method.