The helium plasma in a cylindrical, axially symmetric direct current hollow cathode discharge is theoretically investigated. A self-consistent hybrid method is used to describe the radial behaviour of the plasma components and the electric field around the axial centre of the discharge. The hybrid method includes the solution of an equation system consisting of Poisson's equation and fluid equations for electrons, ions and excited helium atoms. Using the electric field and excited atom densities obtained in this system, the space-dependent transport and collision rate coefficients of the electrons are obtained by a kinetic treatment of the electrons. This treatment is based on a powerful multi-term method for solving the inhomogeneous Boltzmann equation in cylindrical coordinates. The theoretical results obtained for a discharge current of some mA and a pressure of few Torr are compared with available experimental ones.