For longer lifetime of electric propulsion system, an electrodeless plasma thruster with rotating electric field have been proposed utilizing a helicon plasma source. The rotating electric field may produce so-called Lissajous acceleration of helicon plasma in the presence of diverging magnetic field through a complicated mechanism originating from many parameters. Two-dimensional simulations of the Lissajous acceleration were conducted by a code based on Particle-In-Cell (PIC) method and Monte Carlo Collision (MCC) method for understanding plasma motion in acceleration area and for finding the optimal condition. Obtained results show that azimuthal current depends on ratio of electron drift radius to plasma region length, AC frequency, and axial magnetic field. When ratio of cyclotron frequency to the AC frequency is higher than unity, reduction of the azimuthal current by collision effect is little or nothing.