Abstract: Disclosed is a Y-type cylinder-controlled valve assembly which mainly consists of a valve body and a cylinder having a reduced upper portion. The reduced upper portion of the cylinder has an inner diameter smaller than the outer diameter of a piston in the cylinder and thereby serves as a means to define the maximum travel of the piston. Moreover, the valve body has an inclined cylinder-receiving sleeve which has an enlarged inner diameter than that of a conventional Y-type valve assembly and thereby effectively prevents the valve thereof from being frictionally stuck in the inclined sleeve due to any deviation of the valve by fluid passing through the valve body.