Linear programming is required in a wide variety of application including routing, scheduling, and various optimization problems. The primal-dual interior point (PDIP) method is state-of-the-art algorithm for solving linear programs, and can be decomposed to matrix-vector multiplication and solving systems of linear equations, both of which can be conducted by the emerging memristor crossbar technique in O(1) time complexity in the analog domain. This work is the first to apply memristor crossbar for linear program solving based on the PDIP method, which has been reformulated for memristor crossbars to compute in the analog domain. The proposed linear program solver can overcome limitations of memristor crossbars such as supporting only non-negative coefficients, and has been extended for higher scalability. The proposed solver is iterative and achieves O(N) computation complexity in each iteration. Experimental results demonstrate that reliable performance with high accuracy can be achieved under process variations.