  We study a classically scale-invariant model with an electroweak singlet
complex scalar mediator together with an anomaly free set of two fermionic dark
matters. We introduce $U(1)_X$ gauge symmetry with a new charge $X$ in the dark
sector in order to stabilize the mass of the scalar singlet with a new gauge
boson. Our conformally invariant scalar potential generates the electroweak
symmetry breaking via the Coleman-Weinberg mechanism, and the new scalar
singlet acquires its mass through radiative corrections of the fermionic dark
matters and the new gauge boson as well as of the SM particles. Taking into
account the collider bounds, we present the allowed region of new physics
parameters satisfying the recent measurement of relic abundance. With the
obtained parameter sets, we predict the elastic scattering cross section of the
new singlet fermions into target nuclei for a direct detection of the dark
matter. We also discuss the collider signatures and future discovery potentials
of the new scalar and gauge boson.
