This paper contains results of numerical and experimental investigation of glow discharge plasma created in a chamber of a new-type large-volume coaxial gridded hollow cathode. The discharge is created in argon at 25 Pa by applying time-varying power with frequency 20 kHz on electrodes. A 2-D model of the discharge was built using COMSOL Multiphysics. Self-consistent description of the discharge was obtained using the extended fluid approach, which couples continuity equations for charged particles and electron energy balance with Poisson's equation for electric potential. Electron transport coefficients and rates of electron-impact reactions were calculated using the electron energy distribution function. The spatial and radial distributions of plasma potential (V_p), electron density (n_e), and electron temperature (T_e) were obtained. It is shown that the plasma inside the chamber is similar to the negative glow of a dc glow discharge. Comparison of numerical results with the Langmuir probe measurements of electron density and electron temperature is presented and showed a good agreement.