The invention discloses a starting and stopping system hydraulic control device and an automatic gearbox with the starting and stopping system hydraulic control device. The starting and stopping system hydraulic control device comprises a first input node, wherein an outlet of the first input node is connected with the input end of a first one-way valve, the output end of the first one-way valve is connected with a first output node and a second output node, the first output node is used for outputting a pressure oil source to a clutch oil cavity for controlling the engagement of a clutch, a second output node is communicated with an energy accumulator used for storing the pressure oil source, and the energy accumulator is used for guiding the stored pressure oil source into the clutch oil cavity when the automatic gearbox is fast started. Through the arrangement of the energy accumulator, when the automatic gearbox needs to be fast started, the pressure oil source is fast released to the clutch oil cavity through the energy accumulator so that the clutch is fast closed, further, an automobile is fast started, the fast starting requirement after the temporary parking of the automobile can be met, the fuel consumption due to parking of an engine in an idling running mode is favorably reduced, and the energy-saving and emission reduction effects are also achieved.