Disclosed is a curved belt conveyor, which comprises a curved belt between rollers, guide rollers supporting the inner peripheral edge of the curved belt, a driving roller set in the outer peripheral section of the curved belt, a pinch roller for pressing the forward run side of the curved belt against the driving roller, and a pinch roller for pressing the return run side of the curved belt against the driving roller. The pinch rollers are supported with their axial centers inclined with respect to the reference line. With the pinch rollers inclined to contact the curved belt, the outer peripheral section of the curved belt is driven towards the outside of turning, thereby preventing bulging and zigzag movement of the curved belt.