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, characterized in that: 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 (16b, 33a) being opposed to each other; the cooling passage is constituted of at least one streak of a spiral groove formed in such portion of the outer peripheral surface of the sleeve as extends from the axial-direction one end side of the sleeve to the other end side thereof; and the housing includes a supply port communicating with one end of the spiral groove configured to receive the cooling medium and a discharge port communicating with the other end of the spiral groove configured to discharge therefrom the cooling medium having flown through the cooling passage. 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, characterized in that: 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 (16b, 33a) being opposed to each other; the cooling passage is constituted of at least one streak of a spiral groove formed in such portion of the outer peripheral surface of the sleeve as extends from the axial-direction one end side of the sleeve to the other end side thereof; and the housing includes a supply port communicating with one end of the spiral groove configured to receive the cooling medium and a discharge port communicating with the other end of the spiral groove configured to discharge therefrom the cooling medium having flown through the cooling passage. 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 (16b, 33a) being opposed to each other; the cooling passage is constituted of at least one streak of a spiral groove formed in such portion of the outer peripheral surface of the sleeve as extends from the axial-direction one end side of the sleeve to the other end side thereof; and the housing includes a supply port communicating with one end of the spiral groove configured to receive the cooling medium and a discharge port communicating with the other end of the spiral groove configured to discharge therefrom the cooling medium having flown through the cooling passage.