A rotating electric machine comprising: a housing equipped with a first plurality of cooling fins extending toward an output shaft side from an anti-output shaft side end on an outer circumferential surface; an end bracket provided on the anti-output shaft side of the housing; a cooling fan disposed at a central position of the anti-output shaft side; and a fan cover that is inclined so that cooling air from the fan is directed to the housing side, a second plurality of fins (4, 9) on an inner surface of said fan cover or on an outer surface of said end bracket, wherein the second plurality of fins (4, 9) is disposed on the inner circumferential side at an angle along an air direction of the cooling air from the fan that is a turning flow, and on the outer circumferential side, end cross sections of the second plurality of fins (4, 9) face anti-output shaft side end cross sections of the fins of the housing outer circumferential surface without a gap or with a small gap, characterized in that the number of fins of the housing outer circumferential surface is equal to the number of fins (4,9) of said second plurality of fins (4,9), and said second plurality of fins (4, 9) is inclined in the rotary direction of the cooling fan toward the outer circumferential side, wherein the endmost portions on the outer circumferential side of the fins (4,9) are formed to be parallel to a radiation extension line from the center of the end bracket and wherein the fins (4,9) are configured so that an outer circumferential side end cross section of the parallel portion faces an end bracket side end cross section of the fins on the outer circumference of the housing without a gap or with a small gap, and both end cross sections are in close proximity to or in contact with each other. a housing equipped with a first plurality of cooling fins extending toward an output shaft side from an anti-output shaft side end on an outer circumferential surface; an end bracket provided on the anti-output shaft side of the housing; a cooling fan disposed at a central position of the anti-output shaft side; and a fan cover that is inclined so that cooling air from the fan is directed to the housing side, a second plurality of fins (4, 9) on an inner surface of said fan cover or on an outer surface of said end bracket, wherein the second plurality of fins (4, 9) is disposed on the inner circumferential side at an angle along an air direction of the cooling air from the fan that is a turning flow, and on the outer circumferential side, end cross sections of the second plurality of fins (4, 9) face anti-output shaft side end cross sections of the fins of the housing outer circumferential surface without a gap or with a small gap, characterized in that the number of fins of the housing outer circumferential surface is equal to the number of fins (4,9) of said second plurality of fins (4,9), and said second plurality of fins (4, 9) is inclined in the rotary direction of the cooling fan toward the outer circumferential side, wherein the endmost portions on the outer circumferential side of the fins (4,9) are formed to be parallel to a radiation extension line from the center of the end bracket and wherein the fins (4,9) are configured so that an outer circumferential side end cross section of the parallel portion faces an end bracket side end cross section of the fins on the outer circumference of the housing without a gap or with a small gap, and both end cross sections are in close proximity to or in contact with each other.