The matrix shifts of the H-Xe stretching frequency of noble-gas hydrides, HXeCCH, HXeBr, and HXeI in various noble-gas matrices (in Ne, Ar, Kr, and Xe matrices) are investigated via the hybrid quantum-classical simulations. The order of the H-Xe stretching frequencies is found to be ν(gas) < ν(Ne) < ν(Xe) < ν(Kr) < ν(Ar) for HXeCCH and HXeBr, while it is ν(gas) < ν(Ne) < ν(Xe) < ν(Ar) < ν(Kr) for HXeI. This order is anomalous with respect to the matrix dielectric constants, and the calculated results reproduce the experimentally observed shifts quite successfully. We also find that the matrix shifts from the gas-phase values are Δν(HXeCCH) ≈ Δν(HXeCl) < Δν(HXeBr) < Δν(HXeI) in the same noble-gas matrix environments, which implies that the weakly bound molecules exhibit large matrix shifts. The local trapping site is analyzed in detail, and it is shown that a realistic modeling of the surrounding matrix environments is essential to describe the unusual matrix shifts accurately.