Polymer and carbon nanotubes (CNTs) nanocomposites exhibit many properties that are not present in either the pure polymer or CNTs. The polymer crystallization kinetics and crystal forms are greatly changed by dispersion of CNTs nanotubes. In addition to various thermophysical properties, CNTs are metallic or semiconductive and highly anisotropic while the polymer hosts are typically excellent insulators and isotropic. In this work, measurements of the electrical conductivity, σ, of thin-film nanocomposites of isotactic polypropylene (iPP) and CNTs as a function of CNT concentration (0, 1, 2, and 5% by weight of CNT) and melt-shearing induced anisotropy in σ between parallel and perpendicular to the shearing axis is presented and compared them with analogous data for their thermal transport properties. The iPP host is itself one of the most widely used polymers, has liquid crystalline phases, and it is expected that iPP/CNT nanocomposites will be widely used in many polymer applications, some of which are for flexible electrodes, medical and electronics packaging and chemical sensors. The effect of melt-shearing is expected to induce anisotropy in the various properties of the iPP/CNT thin film that should be particularly apparent in the electrical conductivity of the polymer films, higher in the direction of the alignment and lower in the direction perpendicular to it. With increasing CNT content, the average conductivity 〈σ〉 increases slightly from 0 to 2% CNT then dramatically increases by eight orders of magnitude for 5%. The shear induced property of anisotropy, δσs = (σ‖ − σ┴) / 〈σ〉, overall increases with CNT content, revealing a large spike for the 1% sample, indicating the possibility of enhanced δσs due to optimized orienting procedures.