We analyze a classically scale invariant extension of the Standard Model with dark gauge $U(1)_X$ broken by doubly charge scalar $Phi$ leaving a remnant $Z_2$ symmetry. Dark fermions are introduced as dark matter candidates and for anomaly reasons we
introduce two chiral fermions. Due to classical scale invariance, bare mass term that would mix these two states is absent and they end up as stable Majorana fermions $N_1$ and $N_2$. We calculate cross sections for $N_aN_a to phiphi$, $N_aN_a to X^mu phi$ and $N_2N_2 to N_1N_1$ annihilation channels. We put constraints to the model from the Higgs searches at the LHC, dark matter relic abundance and dark matter direct detection limits by LUX. The dark gauge boson plays a crucial role in the Coleman-Weinberg mechanism and has to be heavier then 680 GeV. The viable mass region for dark matter is from 470 GeV up to a few TeV. In the case when two Majorana fermions have different masses, two dark matter signals at direct detection experiments could provide a distinctive signature of this model.
