A hydraulic system for achieving a sequential operation of an engineering vehicle mechanism, comprising: an electric motor (1), a hydraulic pump (2), an electromagnetic reversing valve (3), a sequence valve I (4), a hydraulic execution element I, a sequence valve II (6), and a hydraulic execution element II. The electric motor is connected to the hydraulic pump. The hydraulic pump outputs oil to drive, by means of the electromagnetic reversing valve, the hydraulic execution element I and the hydraulic execution element I to operate. The sequence valve I is connected in series between a large cavity oil port of the hydraulic execution element I and an oil port hydraulic circuit of the electromagnetic reversing valve. The sequence valve II is connected in series between the large cavity oil port of the hydraulic execution element II and the oil port hydraulic circuit of the electromagnetic reversing valve. An electric control portion of the hydraulic system merely needs to control one electromagnetic reversing valve, and the remaining portions are controlled by a hydraulic pressure, so as to achieve sequentiality of movements and control of a speed. The present invention is safe, stable, reliable, low-cost, and suitable for popularization and promotion. Also disclosed are a working method of the hydraulic system and an engineering vehicle comprising the hydraulic system.