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.
Comment: 22 pages, 9 figures, accepted for publication in ApJS