In this work, 9-benzyl-9$H$-carbazole (BzCz) monomer was chemically synthesized by a new process. It was electrocoated on carbon fiber microelectrode (CFME) as an active electrode material in 0.1M sodium perchlorate ($NaClO_4$)/acetonitrile (ACN) solution. The electropolymerization process was successfully performed less amount of 3 mM. The characterization of Poly(BzCz)/CFME thin films was performed by Fourier transform infrared reflectance-attenuated total reflection spectroscopy (FTIR-ATR) and Electrochemical impedance spectroscopy (EIS). The effects of monomer concentrations (1, 2, and 3 mM) during the preparation of modified electrodes were examined by EIS. Capacitive behaviors of modified CFMEs were defined via Nyquist, Bode-magnitude and Bode-phase plots. Variation of capacitance values by initial monomer concentration and specific capacitance values are presented. The highest specific capacitance value for a potensiodynamically prepared polymer thin film in the initial monomer concentration of 1 mM with a charge of 4.54 mC $cm^{-2}$ was obtained about 221.4 ${mu}F;cm^{-2}$. An equivalent circuit model, R(C(R(QR)))(CR), for different concentrations of Poly(BzCz). CFME was proposed and experimental data were simulated to obtain the numerical values of circuit components.