A belt-drive continuously variable transmission having a continuously variable function of making stepless change of a transmission ratio that is a ratio between input speed of an transmission input shaft and output speed of transmission output shaft by changing a contact radius of a belt contacted with a primary pulley and secondary pulley, the primary pulley comprising a primary fixed sheave having a primary fixed sheave shaft and a primary moveable sheave having a primary moveable sheave sleeve, the primary moveable sheave sleeve being fitted onto the primary fixed sheave shaft and slidably moveable relative to the primary fixed sheave shaft in an axial direction of the primary pulley, the secondary pulley comprising a secondary fixed sheave having a secondary fixed sheave shaft and a secondary moveable sheave having a secondary moveable sheave sleeve, the secondary moveable sheave sleeve being fitted onto the secondary fixed sheave shaft and slidably moveable relative to the secondary fixed sheave shaft in an axial direction of the secondary pulley, the belt is wound on the primary pulley and the secondary pulley to transmit a driving force from a drive source to the primary pulley and the secondary pulley; wherein the belt is wound on a pair of primary sheave surfaces (42c, 42d) of the primary fixed sheave and the primary moveable sheave which are opposed to each other to form a V-shaped groove therebetween, and a pair of secondary sheave surfaces (43c, 43d) of the secondary fixed sheave and the secondary moveable sheave which are opposed to each other to form a V-shaped groove therebetween, a first fixed side axial groove extending on an outer circumferential surface of the primary fixed sheave shaft in the axial direction of the primary pulley; a first moveable side axial groove extending on an inner circumferential surface of the primary moveable sheave sleeve in the axial direction of the primary pulley so as to be opposed to the first fixed side axial groove; a first intervening member (14; 18) disposed between the first fixed side axial groove and the first moveable side axial groove, the first intervening member serving to reduce slide resistance that is caused when the primary moveable sheave sleeve makes an axial slide motion in a transmission range between a low transmission ratio and a high transmission ratio, a first axial tapered groove is formed as one end portion of the first fixed side axial groove and tapered toward a side of the primary sheave surface of the primary fixed sheave such that the first axial tapered groove is formed as a part of the first fixed side axial groove which is disposed corresponding to a highest transmission ratio range, and the first axial tapered groove is formed such that a depth defined between the first fixed side axial groove and the first moveable side axial groove is gradually reduced toward a side of a highest transmission ratio, and a first intervening member displacement limiting member (16, 17; 19) arranged to limit an amount of displacement of the first intervening member (14; 18) relative to the primary fixed sheave shaft or the primary moveable sheave sleeve along the first fixed side axial groove or the first moveable side axial groove, characterized in that when the primary moveable sheave sleeve is moved toward a lock position in which the first intervening member (14; 18) is engaged in the first axial tapered groove that is tapered such that the depth between the first fixed side axial groove and the first moveable side axial groove is gradually reduced, the first intervening member (14; 18) serves as a lock member that locks the primary moveable sheave sleeve in a lock position corresponding to the highest transmission ratio, the first intervening member displacement limiting member serves to input an engagement force produced by a hydraulic thrust acting on the primary moveable sheave to the first intervening member (14; 18), and wherein when the primary moveable sheave sleeve is moved apart from the lock position thereof, the first intervening member displacement limiting member (17; 19) serves to input a disengagement force produced by a belt reaction force acting on the primary moveable sheave to the first intervening member (14; 18).