  We study an extension of the Standard Model (SM) which could have two
candidates for dark matter (DM) including a Dirac fermion and a vector dark
matter (VDM) under a new $U(1)$ gauge group in the hidden sector. The model is
classically scale-invariant and the electroweak symmetry breaks because of loop
effects. We investigate the parameter space allowed by current experimental
constraints and phenomenological bounds. We probe the parameter space of the
model in the mass range $1< M_V<5000$ GeV and $1<M_{\psi}<5000$ GeV. It has
been shown that there are many points in this mass range that are in agreement
with all phenomenological constraints. The electroweak phase transition has
been discussed and it has been shown that there is region in the parameter
space of the model consistent with DM relic density and direct detection
constraints that, at the same time, can lead to first order electroweak phase
transition. The gravitational waves produced during the phase transition could
be probed by future space-based interferometers such as LISA and BBO.
