Determining the ages and helium core sizes of red giants is a challenging problem. To estimate the age and helium core size precisely requires a good understanding of the internal structure of the red giant. The properties of the g-dominated mixed modes of red giants are closely related to their inner radiative cores, especially the central helium core. Thus, the g-dominated mixed modes are useful indicators for probing the properties of the helium core and constraining the age of red giants. In our previous work, we have estimated the helium core sizes of the red giants KIC 9145955 and KIC 9970396 by asteroseismic models. In this work, we take a further step to calibrate the ages and core overshooting parameters for these two red giants. We find that the ages of these two stars are 4.61 +/- 0.23 and 6.13 +/- 0.19 Gyr, respectively. From a comparative study, we find that, for a single red giant, the age estimated by the asteroseismology of g-dominated mixed modes is likely to be more precise than that estimated by the combination of the asteroseismic (Delta nu and Delta P (obs)) and spectroscopic (T (eff) and [Fe/H]) observations. In addition, we estimate the core overshooting parameters of these two stars. We find that the overshooting parameter f (ov) of KIC 9145955 and KIC 9970396 was probably overestimated in previous works.