  We compute from quenched lattice QCD the ground state masses of the charmed
hybrid mesons cbar c g, with exotic quantum numbers JPC=1-+, 0+- and 0--. The
0-- hybrid meson spectrum has never been provided by lattice simulations due to
the difficulties to extract high gluonic excitations from noise. We employ
improved gauge and fermion actions on the anisotropic lattice, which reduce
greatly the lattice artifacts, and lead to very good signals. The data are
extrapolated to the continuum limit, with finite size effects under well
control. For 1-+ and 0+- hybrid mesons, the ground state masses are 4.405(38)
GeV and 4.714(52) GeV. We predict for the first time from lattice QCD, the
ground state mass of 0-- to be 5.883(146) GeV.
