  Using Mukhanov-Chamseddine mimetic approach, we study $F(R)$ gravity with
scalar potential and Lagrange multiplier constraint. As we demonstrate, for a
given $F(R)$ gravity and for suitably chosen mimetic potential, it is possible
to realize inflationary cosmology consistent with Planck observations. We also
investigate the de Sitter solutions of the mimetic $F(R)$ theory and study the
stability of the solutions, when these exist, towards linear perturbations,
with the unstable solutions, which can provide a mechanism for graceful exit
from inflation. Finally, we describe a reconstruction method which can yield
the $F(R)$ gravity that can generate realistic inflationary cosmological
evolution, given the mimetic potential and the Hubble rate.
