We have investigated the effect of adding polar rodlike nanoparticles (NPs) to a liquid crystal using Monte Carlo simulations. The mesogens (Ms) are represented with Gay–Berne elongated ellipsoids endowed with a central axial electric dipole. A NP is instead modelled by a overall rod-like set of rigidly assembled Lennard–Jones spherical beads (Orlandi et al. Phys. Chem. Chem. Phys. 18, 2428–2441 (2016). doi:10.1039/C5CP05754J) that are either non-polar or endowed with a central axial dipole of different strengths. We consider two cases: one of strong NP-M affinity and weak NP-NP interactions (case 1) and the opposite one of weak NP-M affinity and strong NP-NP interactions (case 2). We find that for case 1 adding polar NPs slightly lowers the nematic-isotropic transition temperature T NI which instead, for case 2, is essentially unaffected. Having strongly polar, instead of non-polar NPs reduces the T NI difference with the pristine one, while significantly increasing the dielectric anisotropy in the nematic phase, which could be useful in applications.