Two-dimensional Navier-Stokes equation is solved in an analytical way by a perturbation method to investigate incompressible viscous flows between two intersecting permeable walls. The velocity components in cylindrical-polar coordinate system are expressed by means of a stream function, from which two unknown functions for the velocity components are appropriately defined. The perturbation method is applied to seek solutions of the functions. The functions obtained are both described by the forth order ordinary differential equations. In consequence, their function forms are correctly determined up to the first order approximation. The present solution contains Berman's solution for the flow between two permeable parallel plates, which is valid only in the zeroth order approximation. It reduces to the well-known two-dimensional Poiseuille flow between two parallel impermeable walls. It is also shown that the present solution includes Jeffery-Hamel's solution in the special case of impermeable walls for the same spatial configuration as the present one.