  In this work we will extend the inert-doublet model (IDM) by adding a new
$U(1)_{F}$ gauge symmetry to it, under which, a $Z_{2}$ even scalar
($\phi_{2}$) and $Z_{2}$ odd right handed component of two exotic charged
leptons $(F_{eR},\ F_{\mu R})$, are charged. We also add one $Z_{2}$ even real
scalar ($\phi_{1}$) and one complex scalar ($\phi$), three neutral Majorana
right handed fermions ($N_{1},\ N_{2},\ N_{3}$), two left handed components of
the exotic charged leptons $(F_{eL},\ F_{\mu L})$ as well as $F_{\tau}$ are all
odd under the $Z_{2}$, all of which are not charged under the $U(1)_{F}$. With
these new particles added to the IDM, we have a model which can give two scalar
DM candidates, together they can explain the present DM relic density as well
as the muon (g-2) anomaly simultaneously. Also in this model the neutrino
masses are generated at one loop level. One of the most peculiar feature of
this model is that non-travail solution to the axial gauge anomaly free
conditions lead to the prediction of a stable very heavy partner to the
electron ($F_{e}$), whose present collider limit (14 TeV LHC) on its mass
should be around $m_{F_{e}} \geq$ few TeV.
