The steady diffusioosmotic flow of an electrolyte solution in the fibrous porous medium constructed by a homogeneous array of parallel charged circular cylinders is analytically studied. The imposed electrolyte concentration gradient is constant and normal to the axes of the cylinders. The electric double layer surrounding each cylinder may have an arbitrary thickness relative to the radius of the cylinder. A unit cell model which allows for the overlap of the double layers of adjacent cylinders is employed. The electrokinetic equations that govern the ionic concentration distributions, the electrostatic potential profile, and the fluid flow field in the electrolyte solution surrounding the charged cylinder in a unit cell are linearized assuming that the system is only slightly distorted from equilibrium. Through the use of a regular perturbation method, these linearized equations are solved with the surface charge density (or zeta potential) of the cylinder as the small perturbation parameter. Analytical expressions for the diffusioosmotic velocity of the electrolyte solution as a function of the porosity of the ordered array of cylinders correct to the second order of their surface charge density or zeta potential are obtained from a balance between the electrostatic and the hydrodynamic forces exerted on each cylinder. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made. In the limit of maximum porosity, these results can be interpreted as the diffusiophoretic velocity of an isolated circular cylinder caused by the transversely imposed electrolyte concentration gradient.