A hydraulic auto-tensioner comprising: a cylinder having a bottom, and containing oil in the cylinder; a valve sleeve standing on a bottom surface of the cylinder; a rod having a lower end portion slidably inserted in the valve sleeve such that a pressure chamber is defined in the valve sleeve; a spring seat provided on an upper portion of the rod; a return spring mounted between the spring seat and the bottom surface of the cylinder, and biasing the cylinder and the spring seat in a direction away from each other; wherein a reservoir chamber is defined between an inner periphery of the cylinder and an outer periphery of the valve sleeve, and wherein an oil passage is formed such that a lower portion of the pressure chamber communicates with a lower portion of the reservoir chamber through the oil passage, a first check valve provided in a bottom end of the valve sleeve, and configured such that when pressure in the pressure chamber exceeds pressure in the reservoir chamber, the first check valve is closed so as to block communication between the pressure chamber and the oil passage; wherein the hydraulic auto-tensioner is configured such that when a pushing force is applied to the rod through the spring seat, the first check valve is closed so that oil in the pressure chamber leaks from the pressure chamber into the reservoir chamber, and a hydraulic damper force generated by the oil leaking from the pressure chamber dampens the pushing force applied to the rod, characterized in that the hydraulic auto-tensioner further comprises: a tubular plunger fitted on an outer diameter surface of the rod, wherein a first leakage gap is defined between sliding surfaces of the plunger and the rod, the tubular plunger being slidable along the outer diameter surface of the rod and an inner diameter surface of the valve sleeve; wherein a second leakage gap is defined between sliding surfaces of the plunger and the valve sleeve such that resistance to oil flowing in the second leakage gap is larger than resistance to oil flowing in the first leakage gap, a second check valve provided between the rod and the plunger, and configured to close the first leakage gap when the plunger moves upwardly as the pressure in the pressure chamber increases; a stopper provided at a bottom end of the rod so as to prevent separation of the plunger; and a valve spring biasing the plunger toward the stopper. a cylinder having a bottom, and containing oil in the cylinder; a valve sleeve standing on a bottom surface of the cylinder; a rod having a lower end portion slidably inserted in the valve sleeve such that a pressure chamber is defined in the valve sleeve; a spring seat provided on an upper portion of the rod; a return spring mounted between the spring seat and the bottom surface of the cylinder, and biasing the cylinder and the spring seat in a direction away from each other; wherein a reservoir chamber is defined between an inner periphery of the cylinder and an outer periphery of the valve sleeve, and wherein an oil passage is formed such that a lower portion of the pressure chamber communicates with a lower portion of the reservoir chamber through the oil passage, a first check valve provided in a bottom end of the valve sleeve, and configured such that when pressure in the pressure chamber exceeds pressure in the reservoir chamber, the first check valve is closed so as to block communication between the pressure chamber and the oil passage; wherein the hydraulic auto-tensioner is configured such that when a pushing force is applied to the rod through the spring seat, the first check valve is closed so that oil in the pressure chamber leaks from the pressure chamber into the reservoir chamber, and a hydraulic damper force generated by the oil leaking from the pressure chamber dampens the pushing force applied to the rod, a tubular plunger fitted on an outer diameter surface of the rod, wherein a first leakage gap is defined between sliding surfaces of the plunger and the rod, the tubular plunger being slidable along the outer diameter surface of the rod and an inner diameter surface of the valve sleeve; wherein a second leakage gap is defined between sliding surfaces of the plunger and the valve sleeve such that resistance to oil flowing in the second leakage gap is larger than resistance to oil flowing in the first leakage gap, a second check valve provided between the rod and the plunger, and configured to close the first leakage gap when the plunger moves upwardly as the pressure in the pressure chamber increases; a stopper provided at a bottom end of the rod so as to prevent separation of the plunger; and a valve spring biasing the plunger toward the stopper.