The Transiting Exoplanet Survey Satellite (TESS) is an all-sky survey mission aiming to search for exoplanets that transit bright stars. The high-quality photometric data of TESS are excellent for the asteroseismic study of solar-like stars. In this work, we present an asteroseismic analysis of the red-giant star HD 222076 hosting a long-period (2.4 yr) giant planet discovered through radial velocities. Solar-like oscillations of HD 222076 are detected around 203 mu Hz by TESS for the first time. Asteroseismic modeling, using global asteroseismic parameters as inputs, yields a determination of the stellar mass (M-* = 1.12 +/- 0.12 M-circle dot), radius (R-* = 4.34 +/- 0.21 R-circle dot), and age (7.4 +/- 2.7 Gyr), with precisions greatly improved from previous studies. The period spacing of the dipolar mixed modes extracted from the observed power spectrum reveals that the star is on the red-giant branch burning hydrogen in a shell surrounding the core. We find that the planet will not escape the tidal pull of the star and will be engulfed into it within about 800 Myr, before the tip of the red-giant branch is reached.