The invention discloses a hydraulic damper with a rigidity adjustment function. The hydraulic damper comprises a right pin head (1), a right end cover (2), a cylinder body (3), a piston assembly (4), a piston rod (5), a left end cover (6), a left pin head (7), a first valve group (10), a second valve group (11), an oil storage tank assembly (14) and a plurality of oil passing paths. According to the hydraulic damper with the rigidity adjustment function, by the arrangement of a rigidity compensation device on a piston of the hydraulic damper, the requirement for the rigidity in the drawing direction of the hydraulic damper can be met in way of adjusting the structural rigidity of the hydraulic damper or replacing working oil fluid, and then the requirement for the rigidity in the pressing direction of the hydraulic damper can be met in way of adjusting the rigidity compensation device arranged on the piston of the hydraulic damper, thus meeting the requirements for the rigidity in the drawing and pressing directions of the hydraulic damper. The hydraulic damper with the rigidity adjustment function is simple in structure and reliable in work, can meet the requirement for rigidity adjustment in the drawing and pressing directions of the hydraulic damper, and has a wide application prospect.