The invention relates to a construction method for installing a rubber waterstop on an automatic folding type joint box of an underground continuous wall. The method comprises the steps of guide wallconstruction, trench excavation, reinforcement cage binding and lowering, joint box assembling and installation, concrete pouring, joint box contraction and lifting out and the like. A back plate, rear side plates, front side plates and a front plate of the joint box are hinged to each other and are sealed by strip-shaped waterstop, a plurality of folding hydraulic arms are arranged between the rear side plates, a plurality of rubber waterstop clamping devices and clamping hydraulic arms are arranged on the front plate, the folding hydraulic arms and the clamping hydraulic arms are connected with a hydraulic pump through independent hydraulic pipes, and the joint box is connected into a whole through fastening pull rods; after the concrete of the underground continuous wall reaches a certain strength, the folding hydraulic arms are contracted, and the clamping hydraulic arm are stretched synchronously, so that the joint box integrally contracts and folds, the clamping device releases the rubber waterstop, and the joint box is lifted out. The water stop and seepage prevention performance of the joint of the concrete underground continuous wall can be improved, construction is convenient and fast, and economic and social benefits are good.