A dual-shaft hinge with alternative rotation includes: a pivotal base, and having an axial swinging member and a radial moving member; a first core shaft, having a first shaft rod, a first guiding slot and a first latching slot, and the first core shaft is formed in an unlocked status when the first latching slot is engaged with the radial moving member; and a second core shaft, having a second shaft rod, a second guiding slot and at least one second latching slot; the second core shaft is formed in a locked status when the at least one second latching slot is engaged with the radial moving member, and the first core shaft is in the unlocked status, thereby enabling the first core shaft and the second core shaft to alternatively rotate.