  GaTa$_4$Se$_8$ belongs to the lacunar spinel family. Its crystal structures
is still a puzzle though there have been intensive studies on its novel
properties, such as the Mott insulator phase and superconductivity under
pressure. In this work, we investigate its phonon spectra through
first-principle calculations and proposed it most probably has crystal
structure phase transition, which is consistent with several experimental
observations. For the prototype lacunar spinel with cubic symmetry of space
group $F\bar{4}3m$, its phonon spectra have three soft modes in the whole
Brillouin zone, indicating the strong dynamical instability of such crystal
structure. In order to find the dynamically stable crystal structure, further
calculations indicate two new structures of GaTa$_4$Se$_8$, corresponding to
$R3m$ and $P\bar{4}2_{1}m$, verifying that at the ambient pressure, there does
exist structure phase transition of GaTa$_4$Se$_8$ from $F\bar{4}3m$ to other
structures when the temperature is lowered. We also performed electronic
structure calculation for $R3m$ and $P\bar{4}2_{1}m$ structure, showing that
$P\bar{4}2_{1}m$ structure GaTa$_4$Se$_8$ is band insulator, and obtained Mott
insulator state for $R3m$ structure by DMFT calculation under single-band
Hubbard model picture when interaction parameter U is larger than 0.40 eV vs.
band width of 0.25 eV. It is reasonable to assume that while lowering the
temperature, $F\bar{4}3m$ structure GaTa$_4$Se$_8$ becomes $R3m$ structure
GaTa$_4$Se$_8$ first, then $P\bar{4}2_{1}m$ structure GaTa$_4$Se$_8$, because
of the symmetry of $P\bar{4}2_{1}m$ is lower than $R3m$ after Jahn-Teller
distortion. The structure transition may explain the magnetic susceptibility
anomalous at low temperature.
