To provide a manufacturing method of a hydraulic automatic tensioner for timing belt tension adjustment of automobile engine capable of improving wear resistance of a valve sleeve without increasing costs.

One of the following methods is adopted. A method to form a valve sleeve by a process to form a bottomed cylindrical shape by press- working a plate stock and a press working process to finish the formed part within a prescribed dimensional tolerance. A method to form the valve sleeve by a process to form the bottomed cylindrical shape by press-working the plate stock and a turning operation process to finish the formed part within the prescribed dimensional tolerance. A method to form the valve sleeve by conducting one process of press-working for both a process to form the plate stock to the bottomed cylindrical shape and a process to finish the formed part within the prescribed dimensional tolerance.