  In the present paper, it is assumed that there exist two species of dark
matter: a heavy dark matter particle (HDM) with the mass of O(TeV) which is
generated in early universe and a lighter dark matter particle (LDM) which is a
relativistic product due to the decay of HDM. HDMs, captured by the earth,
decay to high energy LDMs, and these particles can be measured by km$^3$
neutrino telescopes, like the IceCube detector. A $Z^{\prime}$ portal dark
matter model is taken for LDMs to interact with nuclei via a neutral current
interaction mediated by a heavy gauge boson $Z^{\prime}$. With the different
lifetimes of decay of HDMs and Z$^{\prime}$ masses, the event rates of LDMs,
measured by IceCube, are evaluated in the energy range between 1 TeV and 100
TeV. According to the IceCube data, the upper limit for LDM fluxes is estimated
at 90\% C.L. at IceCube. Finally, it is proved that LDMs could be directly
detected in the energy range betwen O(1TeV) and O(10TeV) at IceCube with
$m_{Z^{\prime}} \lesssim 500 GeV$ and $\tau_{\phi} \lesssim 10^{21}$ s.
