To provide a hydraulic shock absorber improving comfort of a vehicle by relieving a shock from a road surface even when the shock is caused by high frequency vibration.

A piston 2 provided in a cylinder 1 partitions the inside of the cylinder into a rod side oil chamber 4 on the piston rod side and an anti-rod side oil chamber 5, and two oil chambers communicate with each other through a pair of ports 6, 7 provided in the piston 2. The outlet ends of the pair of ports are provided with damping valves 8, 9 respectively in an openable/closable manner, and a support member 10 holding the piston 2 and the damping valves 8, 9 is movably arranged on the axis of the piston rod 3 and held between stoppers 22, 18 provided on the axis of the piston rod 3, through elastic members 13, 16.