The dc and ac electrical transport property of polyvinyl alcohol-multiwall carbon nanotubes composites has been investigated within a temperature range 77≤T≤300 K and in the frequency range 20 Hz–1 MHz in presence as well as in absence of a transverse magnetic field up to 1 T. The dc conductivity follows variable range hopping model. The magnetoconductivity of the samples changes a sign from positive to negative with an increase in temperature which can be interpreted by the dominancy of the quantum interference effect over the wave function shrinkage effect. The ac conductivity follows a power law whereas the temperature dependence of frequency exponent s can be explained by correlated barrier hopping model. The dielectric behavior of the samples has been governed by the grain and grain boundary resistance and capacitance. The ac conductivity reduces with the application of magnetic field. Although the theoretical model to explain it, is still lacking, we may conclude that this is due to the increase in grain and grain boundary resistance by the application of magnetic field.