In this work, a series of epoxy-terminated butadiene acrylonitrile copolymer (ETBN) liquid rubber-intercalated organic montmorillonite (OMMT)-filled epoxy nanocomposites were prepared. The dispersion of OMMT was studied by X-ray diffraction analysis and transmission electron microscope analysis. The mechanical strength and damping properties of the resultant nanocomposites were characterized by mechanical tests and dynamic mechanical analysis, respectively. Thermal stabilities of the pure and modified epoxy samples were studied by thermogravimetric analysis. Results revealed that the addition of OMMT and ETBN could improve the damping properties greatly and decrease the glass transition temperature (Tg) of the composites while the high tensile strength of composites was still maintained. Besides, with the addition of the second nano-filler (nano-CaCO3 or nano-SiO2) into the nanocomposites, the tensile strength of the nanocomposites was further enhanced without decreasing the high damping properties.