  We realize the weak momentum relaxation in Rindler fluid, which lives on the
time-like cutoff surface in an accelerating frame of flat spacetime. The
translational invariance is broken by massless scalar fields with weak
strength. Both of the Ward identity and the momentum relaxation rate of Rindler
fluid are obtained, with higher order correction in terms of the strength of
momentum relaxation. The Rindler fluid with momentum relaxation could also be
approached through the near horizon limit of cutoff AdS fluid with momentum
relaxation, which lives on a finite time-like cutoff surface in Anti-de
Sitter(AdS) spacetime, and further could be connected with the holographic
conformal fluid living on AdS boundary at infinity. Thus, in the holographic
Wilson renormalization group flow of the fluid/gravity correspondence with
momentum relaxation, the Rindler fluid can be considered as the Infrared
Radiation(IR) fixed point, and the holographic conformal fluid plays the role
of the ultraviolet(UV) fixed point.
