The invention discloses a technological process for continuously producing succinic anhydride and co-producing succinic acid through maleic anhydride catalytic hydrogenation. The whole process comprises three steps, namely, reaction, rectification and hydrolysis, wherein two stages of hydrogenation reactors are used for reaction, a primary hydrogenation reactor is a fixed bed reactor with hydrogen entering from the lower part and reaction liquid exiting from the upper part, and a secondary hydrogenation reactor is a trickle bed reactor with hydrogen and reaction liquid entering from the upper part and exiting from the lower part. The technological process adopts an external circulating heat radiation manner, and reaction heat is uniformly removed, so that the average operation temperature of the whole reactor is effectively controlled, and the reaction temperature in the whole main reactor is balanced. Furthermore, the primary hydrogenation reactor adopts the manner that both the maleic anhydride solution and hydrogen flow upward simultaneously, so that the reaction temperature of the whole reactor is controlled to be balanced, local hot spot temperature is effectively controlled and lowered, and the reactants are prevented from polymerizing and depositing carbon or coking.