In this paper, an expression for the acoustic radiation force on a sphere located on the axis of a zero-order Mathieu beam propagating in an ideal fluid is obtained. The simulation results of different kinds of spherical particles, including rigid spheres, fluid spheres, and elastic spheres, are presented to illustrate the theory. Curves of the acoustic radiation force function versus ka are obtained for different half-cone angles β and ellipticity parameters q of the Mathieu beam. The simulation results reveal that β and q have a direct effect on the acoustic radiation force exerted on a spherical object in an ideal fluid. The acoustic radiation force has negative values for a fluid sphere in a zero-order Mathieu beam when the half-cone angle is β≥60°. The value of the half-cone angle β also affects the direction of the acoustic radiation force for an elastic sphere. When the half-cone angle is set as a constant, the greater the ellipticity parameter is, the slower the decrease in the value of the acoustic radiation force function for a spherical particle. The conclusions of this work may be helpful for the design of acoustic tweezers and may also extend the potential applications of acoustic manipulation technology.