A main spindle apparatus, comprising: a housing; a rotation shaft rotatable relative to the housing; a fixed side bearing having an inner ring externally engaged with one end side of the rotation shaft and an outer ring fixed to the housing; a sleeve arranged within the housing on the other end side of the rotation shaft and movable in the axial direction of the rotation shaft; and a free side bearing having an inner ring externally engaged with the other end side of the rotation shaft and an outer ring internally engaged with the sleeve, characterised in: a cooling passage, allowing a cooling medium to flow therethrough, is formed between the outer peripheral surface of the sleeve and the inner peripheral surface of the housing, the outer and inner peripheral surfaces being opposed to each other; the cooling passage includes a first annular groove arranged on the axial-direction one end side of the sleeve, a second annular groove arranged on the other end side of the sleeve, and a streak of spiral groove having one end communicating with the first annular groove and the other end communicating with the second annular groove, the grooves being formed in the outer peripheral surface of the sleeve or in the inner peripheral surface of the housing; and the cooling medium is supplied to the first annular groove and after having flown through the cooling passage, the cooling medium is discharged from the second annular groove. a housing; a rotation shaft rotatable relative to the housing; a fixed side bearing having an inner ring externally engaged with one end side of the rotation shaft and an outer ring fixed to the housing; a sleeve arranged within the housing on the other end side of the rotation shaft and movable in the axial direction of the rotation shaft; and a free side bearing having an inner ring externally engaged with the other end side of the rotation shaft and an outer ring internally engaged with the sleeve, characterised in: a cooling passage, allowing a cooling medium to flow therethrough, is formed between the outer peripheral surface of the sleeve and the inner peripheral surface of the housing, the outer and inner peripheral surfaces being opposed to each other; the cooling passage includes a first annular groove arranged on the axial-direction one end side of the sleeve, a second annular groove arranged on the other end side of the sleeve, and a streak of spiral groove having one end communicating with the first annular groove and the other end communicating with the second annular groove, the grooves being formed in the outer peripheral surface of the sleeve or in the inner peripheral surface of the housing; and the cooling medium is supplied to the first annular groove and after having flown through the cooling passage, the cooling medium is discharged from the second annular groove. a cooling passage, allowing a cooling medium to flow therethrough, is formed between the outer peripheral surface of the sleeve and the inner peripheral surface of the housing, the outer and inner peripheral surfaces being opposed to each other; the cooling passage includes a first annular groove arranged on the axial-direction one end side of the sleeve, a second annular groove arranged on the other end side of the sleeve, and a streak of spiral groove having one end communicating with the first annular groove and the other end communicating with the second annular groove, the grooves being formed in the outer peripheral surface of the sleeve or in the inner peripheral surface of the housing; and the cooling medium is supplied to the first annular groove and after having flown through the cooling passage, the cooling medium is discharged from the second annular groove.