The production of heavy-flavor quark c((c) over bar) and b((b) over bar) in
pp collisions is described under perturbative quantum chromodynamics frame
work, the extrapolation from hadron-hadron up to nucleus-nucleus collisions
Is based on geometrical model by taking into account the nucleus shadowing
effect. We simulate the heavy quark production, the decay to dilepton and
effects of detection and analysis technique of the pairs, and predict the m
uon rate and the invariant mass spectrum of dimuons that could be detected
in forward region in Pb-Pb collisions at large hadron collider energies.