The invention provides an alternating current machine with lower first-order tooth harmonic and a method for weakening the first-order tooth harmonic of the alternating current machine, by way of determining the chute distance of a rotor or stator according to the ratio of width of a stator slot to the width of a rotor slot when the rotor or the stator adopts the chute structure. By using the method of the invention, on the one hand the alternating current machine with lower first-order tooth harmonic can be obtained, on the other hand the alternating current machine meeting the maximum amplitude requirement of first-order tooth harmonic can be conveniently designed, thus simplifying the design process of the alternating current machine and increasing the work efficiency.