High-pressure structures of tantalum hydrides were investigated over a wide pressure range of 0-300 GPa by utilizing evolutionary structure searches. TaH and TaH2 were found to be thermodynamically stable over this entire pressure range, whereas TaH3, TaH4, and TaH6 become thermodynamically stable at pressures greater than 50 GPa. The dense Pnma (TaH2), R (3) over barm (TaH4), and Fdd2 (TaH6) compounds possess metallic character with a strong ionic feature. For the highly hydrogen-rich phase of Fdd2 (TaH6), a calculation of electron phonon coupling reveals the potential high-T-c superconductivity with an estimated value of 124.2-135.8 K.