  How to hunt for higher $P$-wave states of charmonium is still an open topic
when $2P$ charmonia were identified. {In this work, we present an unquenched
quark model calculation to illustrate the spectroscopy behavior of these $3P$,
$4P$ and $5P$ states in charmonium family.} For the $3P$ charmonia, the
predicted masses are around 4.2 GeV and their two-body open-charm decay
behaviors were given, by which we propose that searching for these $3P$ states
via their open-charm decay channels from $\gamma\gamma$ fusion and $B$ decay
can be accessible at future experiment like LHCb and Belle II. We continue to
calculate the masses of these $4P$ and $5P$ charmonia. Combing with these
calculated results of higher $P$-wave states of charmonium, we find that the
coupled-channel effect becomes more obvious with increasing the radial quantum
number, which can be understood well by the modified Godfrey-Isgur model with
screened potential.
