  We extend the idea of mimetic gravity to a Randall-Sundrum II braneworld
model. As for the 4-dimensional mimetic gravity, we isolate the conformal
degree of freedom of 5-dimensional gravity in a covariant manner. We assume the
bulk metric to be made up of a non-dynamical scalar field $\Phi$ and an
auxiliary metric $\tilde{{\cal{G}}}_{AB}$ so that ${\cal{G}}_{AB}=
\tilde{{\cal{G}}}^{CD}\,\Phi_{,C}\,\Phi_{,D}\,\tilde{{\cal{G}}}_{AB}$ where $A,
B, ...$ are the bulk spacetime indices. Then we show that the induced conformal
degree of freedom on the brane as an induced scalar field, plays the role of a
mimetic field on the brane. In fact, we suppose that the scalar degree of
freedom which mimics the dark sectors on the brane has its origin on the bulk
scalar field, $\Phi$. By adopting some suitable mimetic potentials on the
brane, we show that this brane mimetic field explains the late time cosmic
expansion in the favor of observational data: the equation of state parameter
of this field crosses the cosmological constant line in near past from
quintessence to phantom phase in a redshift well in the range of observation.
We show also that this induced mimetic scalar field has the capability to
explain initial time cosmological inflation. We study parameter space of the
models numerically in order to constraint the models with Planck2015 data set.
