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Using the absolute ages of passively evolving galaxies observed at differentredshifts, one can obtain the differential ages, the derivative of redshift $z$with respect to the cosmic time $t$ (i.e. ${\rm d} z/{\rm d}t$). Thus, theHubble parameter $H(z)$ can be measured through the relation $H(z)=-({\rm d}z/{\rm d}t)/(1+z)$. By comparing the measured Hubble parameter at differentredshifts with the theoretical one containing free cosmological parameters, onecan constrain current cosmological models. In this paper, we use this method topresent the constraint on a spatially flat Friedman-Robert-Walker Universe witha matter component and a holographic dark energy component, in which theparameter $c$ plays a significant role in this dark energy model. Firstly weconsider three fixed values of $c$=0.6, 1.0 and 1.4 in the fitting of data. Ifwe set $c$ free, the best fitting values are $c=0.26$, $\Omega_{\rm m0}=0.16$,$h=0.9998$. It is shown that the holographic dark energy behaves like aquintom-type at the $1\sigma$ level. This result is consistent with some otherindependent cosmological constrains, which imply that $c<1.0$ is favored. Wealso test the results derived from the differential ages using anotherindependent method based on the lookback time to galaxy clusters and the age ofthe universe. It shows that our results are reliable.Comment: 18 pages including 7 figures and 1 tables. Final version for  publication in Modern Physics Letters A (MPLA)[minor revision to match the  appear version

CONSTRAINTS ON HOLOGRAPHIC DARK ENERGY MODELS USING THE DIFFERENTIAL AGES OF PASSIVELY EVOLVING GALAXIES