High-pressure phase-transition behaviors of z-cut lithium tantalate single-crystal have been studied by Hugoniot measurements at our two-stage light-gas gun and DFT-PWP calculations. A distinct discontinuity was discovered on the D-u (shock-wave velocity versus particle velocity) relation. An elastic-plastic two-wave structure was observed from the VISAR measured particle velocity profiles at low pressures (25.9 GPa and 32.6 GPa), while three-wave structure appeared in the measured particle velocity profiles at the final pressure of 42.9 GPa and 53.0 GPa. Both facts indicate a shock-induced phase transition of LiTaO3 samples occurred with an onset pressure of 37.9GPa. The theoretically calculated 0K pressure versus compression ratio (P-V/V0) curve for the rhombohedral phase (R3c space group) is in good agreement with the low-pressure experimental data, while that for orthorhombic phase (Pbnm space group) is in accord with the results by deducing thermal pressure contribution from the measured shock-compression data at high pressures. This suggests that the high-pressure phase has orthorhombic symmetry. High-pressure phase transformation behaviors including the transition pressure and structures, which are unclear in current literature, have been clarified in this paper by our new shock-wave data and ab-initio calculations. These behaviors were demonstrated to be in close similarity with that of its isomorphous crystal LiNbO3. The present work is significant for the investigations of shock-induced phase-transition of similar single-crystal materials.