The phenomena of the heavy-fermion superconductivity (HFS) of CeCu2Si2 and UBe13 were theoretically inveotigated by starting from the periodic Anderson lattice model and considering the interaction between the localized electrons and the localized lattice deformation. Throngh the calculations, we obtained a reasonable superconducting transition temperature Tc and showed that the parameter which describes the isotopic effect a<1/2, even equals to zero (in BCS theory a = 1/2). We showed that the isotopic effect is smaller in our theory than that in BCS theory, even there could exist no isotopic effect in our model, the result is in agreement with the experimental facts of HFS. In addition, the curves of the order parameters varing with the temperature and the density of state are given and the conclusion of f-electrons to be responsible for HFS can be obtained naturally.