  In the framework of Left-Right symmetric model, we investigate an interesting
scenario, in which the so-called VEV seesaw problem can be naturally solved
with Z_2 symmetry. In such a scenario, we find a pair of stable weakly
interacting massive particles (WIMPs), which may be the cold dark matter
candidates. However, the WIMP-nucleon cross section is 3-5 orders of magnitude
above the present upper bounds from the direct dark matter detection
experiments for $m \sim 10^2-10^4 $ GeV. As a result, the relic number density
of two stable particles has to be strongly suppressed to a very small level.
Nevertheless, our analysis shows that this scenario can't provide very large
annihilation cross sections so as to give the desired relic abundance except
for the resonance case. Only for the case if the rotation curves of disk
galaxies are explained by the Modified Newtonian Dynamics (MOND), the stable
WIMPs could be as the candidates of cold dark matter.
