The electrokinetic flow of a salt-free solution in the fibrous porous medium constituted by an array of parallel charged circular cylinders subject to a pressure gradient and an electric field imposed in the axial direction is analytically studied via the use of a unit cell model. The Poisson-Boltzmann equation and modified Navier-Stokes equation applicable to a unit cell accommodating the salt-free solution around an individual cylinder are solved to determine the electric potential profile and fluid velocity distribution. Results of the electroosmotic velocity and effective electric conductivity in the fiber matrix are obtained as functions of the surface charge density of the dielectric cylinders and the porosity of the fiber matrix. The effects of the porosity or interactions among the cylinders on the electric potential distribution, electroosmotic velocity, and effective electric conductivity are significant and interesting under practical conditions. The apparent zeta potential, electroosmotic velocity, and effective electric conductivity increase monotonically with an increase in the surface charge density of the cylinders. When the porosity of the fiber matrix and surface charge density of the cylinders are high, the increases of the apparent zeta potential and electroosmotic velocity with the surface charge density are substantially suppressed due to the counterion condensation effect. However, this effect becomes weak when the porosity is low.