To obtain a stationary state of quantum walks, which have eigenvalues on the unit circle, from a natural initial state, we add the infinite length tails to the finite graph, and insert the free quantum walkers as the inflow from these tails to the internal graph. Then we show that if the underlying random walk is reversible, then the scattering on the surface of the internal graph can be expressed by a unitary matrix determined only by the information of the surface, and the stationary state is described by a convex combination of the reversible measure of the random walk and the current flow induced by the graph setting. On the other hand, if the underlying random walk is non reversible, then the scattering on the surface is a perfect reflection and the stationary state is similar to the current flow but satisfies a different type of Kirchhoff's law.