  Cosmological observables could be used to construct cosmological models,
however, a fixed number of observables limited on the light cone is not enough
to uniquely determine a certain model. A reconstructed spherically symmetric,
inhomogeneous model that share the same angular-diameter-distance-redshift
relationship $d_A(z)$ and Hubble parameter $H(z)$ besides $\Lambda\textrm{CDM}$
model (which we call LTB-$\Lambda\textrm{CDM}$ model in this paper), may
provide another solution. Cosmic age, which is off the light cone, could be
employed to distinguish these two models. We derive the formulae for age
calculation with origin conditions. From the data given by 9-year WMAP
measurement, we compute the likelihood of the parameters in these two models
respectively by using the Distance Prior method and do likelihood analysis by
generating Monte Carlo Markov Chain for the purpose of breaking the degeneracy
of $\Omega_m$ and $H_0$ (the parameters that we use for calculation). The
results yield to be: $t_{\Lambda\textrm{CDM}} =13.76 \pm 0.09 ~\rm Gyr$,
$t_{\rm {LTB}-\Lambda\textrm{CDM}} =11.38 \pm 0.15 ~\rm Gyr$, both in $1\sigma$
agreement with the constraint of cosmic age given by metal-deficient stars. The
cosmic age method that is set in this paper enables us to distinguish between
the inhomogeneous model and $\Lambda\textrm{CDM}$ model.
