  In this paper we have considered a red-shift based linear correction in
derivative of action in the context of vacuum $f(R)$ gravity. Here we have
found out that the linear correction may describe the late time acceleration
which is appeared by SNeIa with no need of dark energy. Also we have calculated
the asymptotic action for the desired correction. The value of all solutions
may reduce to de' Sitter universe in the absence of correction term.
