Ionic liquid ion sources have the capability of generating diverse heavy molecular ions, and their applications have been investigated in the field of ion thrusters. This study aims to determine the quality parameters of ionic liquid ion beams and establish methods for their control. Firstly, the beam acceleration process in an ionic liquid ion source was simulated using Particle-in-Cell (PIC) simulation methods, and the effects of the beam current, acceleration voltage, and emitter-extraction gap on the beam emittance and Twiss parameters were investigated. The results indicate that the normalized emittance decreases with a reduction in the beam current and emitter-extraction gap, as well as with an increase in the acceleration voltage. The kinetic energy broadens during the acceleration process. The acceleration efficiency is not obviously affected by the beam current or acceleration voltage. However, it increases with the expansion of the emitter-extraction gap. Secondly, the control of a centimeter-scale beam was simulated by utilizing the beam parameters derived from the simulation of the acceleration process. The results demonstrate that the divergence, velocity distribution, and specific impulse can be controlled by a set of three-electrode electrostatic lenses without imposing additional demands on the power source on the ionic liquid electric thruster.