  Variability is a prominent observational feature of blazars. The high-energy
radiation mechanism of jets has always been important but still unclear. In
this work, we performed a detailed analysis using Fermi-LAT data across 15
years and obtained GeV light curve information for 78 TeV blazars detected by
Fermi. We provided annual GeV fluxes and corresponding spectral indices for the
78 TeV blazars and thorough monthly GeV fluxes for a subsample of 41 bright
blazars. Our results suggest a strong correlation between the ${\gamma}$-ray
photon index and $\log L_{\rm \gamma}$ for the flat spectrum radio quasars
(FSRQs) and high-energy-peaked BL Lacs (HBLs). 14 sources in our sample show
significant GeV outbursts/flares above the relatively stable, low-flux light
curve, with 6 of them showing a clear sharp peak profile in their 5-day binned
light curves. We quantified the variability utilizing the fractional
variability parameter $F_{\mathrm{var}}$, and found that the flux of the FSRQs
showed significantly stronger variability than that of the BL Lacs. The 41
bright blazars in this work are best fit by a log-normal flux distribution. We
checked the spectral behavior and found 11 out of the 14 sources show a
'bluer-when-brighter (BWB)' trend, suggesting this spectral behavior for these
TeV blazars at the GeV band arises from the mechanism that the synchrotron-self
Compton (SSC) process dominates the GeV emission. Our research offers a
systematic analysis of the GeV variability properties of TeV blazars and serves
as a helpful resource for further associated blazar studies.
