To compute the rate coefficients of the hydrogen abstraction of chlorine plus methane (Me), ethane (Et), and propane (Pr), extensive ring-polymer molecular dynamics (RPMD) calculations are performed in conjunction with the potential energy surface of Cl + Me (J. Chem. Phys. 2006, 124, 124306). To treat Cl + Et and Cl + Pr, the recently proposed coarse-grained treatment (J. Chem. Phys. 2017, 146, 024108) of RPMD is used. Compared with previous results, good agreement can be found. Several probable reasons for the temperature dependence feature of the rate coefficients of the heavy-light-heavy reactions are discussed through a mass coupling model.