In this paper, we present the simulations of an electrostatic quadrupole quadruplet (EQQ) lens system that will be used in a new sub-micron multi-ion beam for radiobiological studies. The new sub-micron beam will be used to carry out fine controlled irradiation of sub-cellular matrix with a variety of ions (H + , He 2+ , C 6+ ) with energies up to 3 MeV/charge. Simulations using the SIMION 8.1 ® have shown that the EQQ lens system, configured with a symmetry normally used in a "Russian quadruplet", can achieve a demagnification factor (Df) of 33 at a working distance (Dw) of ~ 98 mm for a 3MeV/charge ion beam. Such focusing strength is comparable to the separated EQ sextuplet (EQS) lens system used in the sub-micron ion beam at Columbia university (Df ~ 38 and Dw ~ 126 mm) [1], but with a more compact lens design and two fewer quadrupoles. Calculations show that the chromatic and the spherical aberration of the EQQ lens system is comparable to those of the EQS lens system. This indicates that the EQQ lens system may be able to give a performance equivalent to the EQS in the Columbia University micro-ion beam when the object aperture is less than or equal to 30 μm. The compact design is expected to allow for precise alignment of the quadrupole electrodes and is intended to achieve stable micron beam spots at the target position.