A hydraulic auto-tensioner for use with an engine accessory, comprising: a cylinder containing hydraulic oil and including a bottom portion having an upper surface formed with a sleeve fit-in hole; a sleeve having a lower end portion press-fitted in the sleeve fit-in hole; a rod having a lower end portion slidably inserted in the sleeve and defining a pressure chamber in the sleeve; a return spring incorporated between a spring washer provided at an upper part of the rod and the upper surface of the bottom portion of the cylinder and biasing the cylinder and the rod in a direction in which the rod protrudes from the cylinder; a tubular spring cover provided on the spring washer and covering an upper part of the return spring; a seal member incorporated in an upper side opening of the cylinder and having an inner periphery kept in elastic contact with an outer periphery of the spring cover, thereby defining a reservoir chamber between the cylinder and the sleeve; wherein at least one oil passage is defined between fitting surfaces of the sleeve and the sleeve fit-in hole such that the reservoir chamber communicates with the pressure chamber through the oil passage; and a check valve mounted in the lower end portion of the sleeve and configured to be closed, thereby disconnecting the pressure chamber from the oil passage, when a pressure in the pressure chamber becomes higher than a pressure in the reservoir chamber, wherein the sleeve has a lower end face in abutment with a bottom surface of the sleeve fit-in hole, characterized in that the bottom surface of the sleeve fit-in hole is stepped so that an outer peripheral portion of the bottom surface is at an upper level than an inner peripheral portion of the bottom surface, and the lower end face of the sleeve is in abutment with the outer peripheral portion of the bottom surface, wherein the bottom surface is stepped by placing an annular washer having a rectangular cross-section on the bottom surface. a cylinder containing hydraulic oil and including a bottom portion having an upper surface formed with a sleeve fit-in hole; a sleeve having a lower end portion press-fitted in the sleeve fit-in hole; a rod having a lower end portion slidably inserted in the sleeve and defining a pressure chamber in the sleeve; a return spring incorporated between a spring washer provided at an upper part of the rod and the upper surface of the bottom portion of the cylinder and biasing the cylinder and the rod in a direction in which the rod protrudes from the cylinder; a tubular spring cover provided on the spring washer and covering an upper part of the return spring; a seal member incorporated in an upper side opening of the cylinder and having an inner periphery kept in elastic contact with an outer periphery of the spring cover, thereby defining a reservoir chamber between the cylinder and the sleeve; wherein at least one oil passage is defined between fitting surfaces of the sleeve and the sleeve fit-in hole such that the reservoir chamber communicates with the pressure chamber through the oil passage; and a check valve mounted in the lower end portion of the sleeve and configured to be closed, thereby disconnecting the pressure chamber from the oil passage, when a pressure in the pressure chamber becomes higher than a pressure in the reservoir chamber, wherein the sleeve has a lower end face in abutment with a bottom surface of the sleeve fit-in hole, characterized in that the bottom surface of the sleeve fit-in hole is stepped so that an outer peripheral portion of the bottom surface is at an upper level than an inner peripheral portion of the bottom surface, and the lower end face of the sleeve is in abutment with the outer peripheral portion of the bottom surface, wherein the bottom surface is stepped by placing an annular washer having a rectangular cross-section on the bottom surface.