A novel hybrid membrane was developed on the basis of poly(m-phenylene isophthalamide) (PA) by introducing an original complex modifier into the polymer; this modifier consisted of equal amounts of heteroarm star macromolecules with a fullerene C60 core (HSM) and the ionic liquid [BMIM][Tf2N] (IL). The effect of the (HSM:IL) complex modifier on characteristics of the PA membrane was evaluated using physical, mechanical, thermal, and gas separation techniques. The structure of the PA/(HSM:IL) membrane was studied by scanning electron microscopy (SEM). Gas transport properties were determined by measuring He, O2, N2, and CO2 permeation through the membranes based on PA and its composites containing a 5 wt% modifier. The permeability coefficients of all gases through the hybrid membranes were lower than the corresponding parameters for the unmodified membrane, whereas the ideal selectivity in the separation of He/N2, CO2/N2, and O2/N2 gas pairs was higher for the hybrid membrane. The position of the PA/(HSM:IL) membrane on the Robeson’s diagram for the O2/N2 gas pair is discussed.