Conducting polyaniline PANI has been obtained inside dielectric nanoporous coordination polymer MIL-101. The application of an electric field transforms both bulk PANI and nanocomposite PANI@MIL to a metastable high-conductive state. After a decrease in the applied electric field, PANI and PANI@MIL relax toward a state low-conductive stable by the law ln[σ(t)/σ(τ)] = −(t/τ)n, which is typical of disordered systems with the characteristic time τ of about six hours for PANI and with three times larger time for composite PANI@MIL. The temperature dependences of the electrical conductivity σ(T) of the samples in both high- and low-ohmic states are described by the fluctuation-induced conductivity model. Significant changes in relaxation processes and in the parameters of the fluctuation-induced tunneling conduction in nanocomposite PANI@MIL are due to a decrease in the sizes of polyaniline particles in the MIL-101 matrix to nanometers.