The broadband dispersion relation of active phonon-polaritons was studied in a ferroelectric lithium tantalate crystal. The reflectivity in the far- and mid-IR regions was measured by the reflection FT-IR measurement. The real and imaginary parts of a reflective index were calculated in the broadband frequency range between 3 and 36 THz. Using these values the dispersion relation of phonon-polariton including damping of polariton was determined using real and imaginary parts of a polariton wave vector. These phonon-polaritons with A1(z) and E(x,y) symmetry are infrared and Raman active. The observed polariton dispersion relation is in agreement within the experimental uncertainty with the phonon-polariton dispersion determined by the previous forward Raman scattering measurements.