1-Butyl 3-methylimidazolium bis(trifluoromethylsulfonyl) imide (BMI)-modified multiwalled carbon nanotubes (MWCNTs) were used as nanofillers for the hydrogenated carboxylated nitrile-butadiene rubber/hydrogenated nitrile-butadiene rubber (HXNBR/HNBR) blends. The multifunctional properties of rubber nanocomposites with various filler loadings were investigated. It was found that in the presence of BMI-MWCNTs, the mechanical strength, dielectric properties, electrical and thermal conductivities of HXNBR/HNBR were significantly improved due to the better dispersibility as well as the intrinsic reinforcement effect of MWCNTs. Particularly, in comparison with unfilled rubber blend, the electrical conductivity of BMI-MWCNTs-filled HXNBR/HNBR composites exhibited three orders of magnitude enhancement with a lower electrical percolation threshold. The tensile strength and thermal conductivity of composites filled with 5 phr (parts per hundred rubber) BMI-MWCNTs increased by 52 and 23%, respectively. In addition, the polarizability of composites was also intensified under the applied electric field, which resulted in remarkable dielectric relaxation compared to neat rubber. Our experimental data have indicated that BMI-MWCNTs can be used as a promising candidate for fabricating multifunctional HXNBR/HNBR nanocomposites.