In this paper, we present a new object matching algorithm based on linear programming and a novel locally affine-invariant geometric constraint. Previous works have shown possible ways to solve the feature and object matching problem by linear programming techniques , . To model and solve the matching problem in a linear formulation, all geometric constraints should be able to be exactly or approximately reformulated into a linear form. This is a major difficulty for this kind of matching algorithms. We propose a novel locally affine-invariant constraint which can be exactly linearized and requires a lot fewer auxiliary variables than the previous work  does. The key idea behind it is that each point can be exactly represented by an affine combination of its neighboring points, whose weights can be solved easily by least squares. The resulting overall objective function can then be solved efficiently by linear programming techniques. Our experimental results on both rigid and non-rigid object matching show the advantages of the proposed algorithm.