A process method for recovering maleic anhydride. In this method, n-butanol is esterified with the gas containing maleic anhydride to produce monoester, and then the monoester is decomposed into n-butanol and maleic anhydride. The characteristic of the process is to set up a thermal decomposition reaction distillation column, which takes monoester and certain content of diester produced by esterification reaction as raw materials, carries out reactive distillation in the tower under corresponding working conditions, n-butanol is produced from the top of the tower, and the esterification reaction tower is recycled, and maleic anhydride and diester are produced at the bottom of the tower for maleic anhydride refining in the fine distillation column. It has the characteristics of fast absorption, high absorption yield, no corrosion of equipment, no three wastes, energy saving and reliable operation.