The present invention discloses a delayed closing system of an intake valve of a double-mode slide valve engine. The delayed closing system comprises a base, a hydraulic tappet assembly and an oil supply system; wherein, the hydraulic tappet assembly can slide up and down along the base; the top of the hydraulic tappet assembly is connected with a valve rocker; the lower end of the hydraulic tappet assembly is connected with an engine camshaft; the oil supply system supplies oil to the hydraulic tappet assembly; an oil-feeding assembly hole and oil-discharging assembly holes are formed on thehydraulic tappet assembly; an oil-feeding hole, one end of which is communicated with the oil supply system and the other end of which is communicated with the oil-feeding assembly hole of the hydraulic tappet assembly, is formed on the base; and oil-discharging holes, which are correspondingly communicated with the oil-discharging assembly holes of the hydraulic tappet assembly, are formed on the base as well. The delayed closing system, which has the advantages of few parts, simple structure, safe and reliable operation and low cost, can realize the mutually independent adjustment of the intake and exhaust of cylinders in order to exert the flexibility of intake phase adjustment to the max and optimize the performance of the engine, the operation process is controlled by a mechanic slide valve mode, the service lives of the elements are long, and the industrialization of the technique can be easily realized.