GaTa4Se8 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 firstprinciple 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 43m, 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 GaTa4Se8, corresponding to R3m and P 421m, verifying that at the ambient pressure, there does exist structure phase transition of GaTa4Se8 from F 43m to other structures when the temperature is lowered. We also performed electronic structure calculation for R3m and P 421m structure, showing that P 421m structure GaTa4Se8 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 43m structure GaTa4Se8 becomes R3m structure GaTa4Se8 first, then P 421m structure GaTa4Se8, because of the symmetry of P 421m is lower than R3m after Jahn-Teller distortion. The structure transition may explain the magnetic susceptibility anomalous at low temperature.