  Classical scale invariance is one of the possible solutions to explain the
origin of the electroweak scale. The simplest extension is the classically
scale-invariant standard model augmented by a multiplet of gauge singlet real
scalar. In the previous study it was shown that the properties of the Higgs
potential deviate substantially, which can be observed in the International
Linear Collider. On the other hand, since the multiplet does not acquire vacuum
expectation value, the singlet components are stable and can be dark matter. In
this letter we study the detectability of the real singlet scalar bosons in the
experiment of the direct detection of dark matter. It is shown that a part of
this model has already been excluded and the rest of the parameter space is
within the reach of the future experiment.
