The influence of cupric oxide (CuO) nanostructures on the thermal conductivity of deionized (DI)water and ethylene glycol (EG) was investigated here. CuO nanospheres (average diameter 7nm) and nanorods (LxW=approximate to 120nmx4nm) have been synthesized; their structural and morphological characterizations have been done by powder x-ray diffraction (XRD), UV-visible spectrophotometer, and transmission electron microcopy (TEM). The CuO nanospheres and nanorods have been dispersed separately in DI water and EG with four different volume fractions (0.005-0.1%). The results showed that an enhancement in thermal conductivity for CuO nanospheres and CuO nanorods was found to be 15% and 17% with respect to DI water, 19% and 21% with respect to EG. The enhancement in thermal conductivity in case of CuO nanorods is due to large surface area, crystallinity, and network formation of nanorods in base fluids which directly help in the transfer of phonon vibrations rapidly from one atom to another atom and increase the heat-transfer rate. Thus, the CuO-EG based-nanofluids exhibited 4-5% higher thermal conductivity than CuO-DI water based nanofluids, nanorods always showed higher thermal conductivity (2-3%) than nanospheres in both base fluids.