Abstract The impedance, modulus spectroscopy and dielectric properties of polyaniline (PANI) and composite with multi-walled carbon nanotube (MWCNT) of different degrees of functionalization are studied from 300 to 4.2 K in the frequency range 40 Hz–5 MHz. At low temperature (T ⩽ 100 K), grain and grain boundary relaxation peaks are observed in PANI. In composites, MWCNT forms a network between less and highly conducting grains, increases dc conductivity, and shows no relaxation peak at low temperature. The chemical functionalization of MWCNT increases the polar interaction between MWCNT and PANI, shifts the relaxation peaks towards lower frequency and slows the relaxation process. The relaxation process is manifested as non-Debye type and it tends towards Debye type with increasing temperature in functionalized muti-walled carbon nanotube (fMWCNT) PANI composites, and explained by Bergman’s theory. The relaxation barrier energy at the interface of fMWCNT and PANI increases with increasing degree of functionalization which is the effect of enhanced interfacial (Maxwell Wagner–Sillars) polarization. In MWCNT composite, the real part of dielectric constant shows high negative value below 10 K at lower frequency ( < 950 Hz) and it becomes positive due to functionalization of MWCNT. An additional crossover from positive to negative occurs in both MWCNT and fMWCNT, PANI composite above temperature 60 K and frequency 500 Hz. This crossover shifts towards higher temperature and frequency with increasing degree of functionalization. The negative value and crossover of dielectric constant are explained by Drude–Sommerfeld model.