G 29 − 38 (TIC 422526868) is one of the brightest (V = 13.1) and closest (d = 17.51 pc) pulsating white dwarfs with a hydrogen-rich atmosphere (DAV/ZZ Ceti class). It was observed by the TESS spacecraft in sectors 42 and 56. The atmosphere of G 29 − 38 is polluted by heavy elements that are expected to sink out of visible layers on short time-scales. The photometric TESS data set spans ∼51 d in total, and from this, we identified 56 significant pulsation frequencies, that include rotational frequency multiplets. In addition, we identified 30 combination frequencies in each sector. The oscillation frequencies that we found are associated with g-mode pulsations, with periods spanning from ∼ 260 to ∼ 1400 s. We identified rotational frequency triplets with a mean separation δνl = 1 of 4.67 μHz and a quintuplet with a mean separation δνl = 2 of 6.67 μHz, from which we estimated a rotation period of about 1.35 ± 0.1 d. We determined a constant period spacing of 41.20 s for l = 1 modes and 22.58 s for l = 2 modes. We performed period-to-period fit analyses and found an asteroseismological model with M∗/M∘ = 0.632 ± 0.03, Teff = 11 635 ± 178 K, and log g = 8.048 ± 0.005 (with a hydrogen envelope mass of MH ∼ 5.6 × 10−5M∗), in good agreement with the values derived from spectroscopy. We obtained an asteroseismic distance of 17.54 pc, which is in excellent agreement with that provided by Gaia (17.51 pc).