The production of heavy-flavor quark c(c̄) and b(b̄) in pp collisions is described under perturbative quantum chromodynamics framework, 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 muon rate and the invariant mass spectrum of dimuons that could be detected in forward r...