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Linear programming (LP) decoding is getting more and more attention because of the maximum-likelihood (ML) certificate property. As one of the improved LP decoding methods, multistage LP (MLP) decoding has been proposed to improve the performance of LP decoding but at the cost of higher complexity. In this paper, the problem of achieving a balance between the performance and the complexity of LP decoding is considered. First, a criterion used for searching new constraints adaptively is proposed. Then a modified MLP decoding is presented by incorporating the adaptive decoding algorithm to decrease the complexity. The presented modified MLP decoding can obtain a good tradeoff between the performance and the complexity and is proved also has the ML certificate characteristic. Simulations with moderate block length LDPC codes show that the proposed MLP decoding achieves the same BER performance as the original MLP decoding with far fewer used constraints and faster convergence speed consequently.