We report the ac conductivity measurement of polyaniline (PANI) composites with carbon nanotubes (CNT) and functionalized carbon nanotubes (fCNT) with different degrees of functionalization from 300 K-4.2 K in the frequency range 40 Hz-5 MHz. The ac conductivity of PANI follows the universal power law and the charge transport is dominated by small polaron tunneling. In the CNT/PANI composite, metallic behaviour emerges, and ac conductivity does not obey the power law which is explained by the Drude model. Due to the chemical functionalization of CNT, disordered semiconducting behaviour appears in the transport below 50 K and follows the Johnscher’s power law. The enhancement of polaron formation due to the polar interaction between fCNT and PANI is reflected in the ac conductivity of the composites. The charge transport is manifested by single electron tunneling for a lower degree of fCNT/PANI (6 h) composite which changes to small polaron tunneling transport for a higher degree of fCNT/PANI (48 h) composite. The dc conductivity behaviour is explained by Mott’s VRH model and the characteristic Mott temperature increases with an increasing degree of chemical functionalization.