A normally-closed valve having a microflow rate adjusting device includes a valve stem for opening and closing a fluid passage; a biasing device for biasing the valve stem in a direction to close the fluid passage; a piston body which is engaged in a cylinder in an air-tight manner to form a pressure chamber for moving the valve stem in a valve opening direction against the biasing device; and a stopper mechanism, provided on the cylinder, for controlling a limit of movement of the piston body in the valve opening direction. The stopper mechanism comprises a stroke adjustment member which is screw-engaged with the cylinder coaxially with the valve stem so that a position of the stroke adjustment member relative to the cylinder can be adjusted, and includes an annular tapered surface at an end of the stroke adjustment member which faces the piston body.