  In this paper, we will solve the Leray's problem for the stationary
Navier-Stokes system in a 2D infinite distorted strip with the Navier-slip
boundary condition. The existence, uniqueness, regularity and asymptotic
behavior of the solution will be investigated. Moreover, we discuss how the
friction coefficient affects the well-posedness of the solution. Due to the
validity of the Korn's inequality, all constants in each a priori estimate are
independent of the friction coefficient. The main novelty is the total flux of
the velocity can be relatively large (proportional to the {\it slip length})
when the friction coefficient of the Navier-slip boundary condition is small,
which is essentially different from the 3D case.
