  We used TESS light curves and HARPS-N spectrograph radial velocity
measurements to establish the physical properties of the transiting exoplanet
candidate found around the star HD 20329 (TOI-4524). We performed a joint fit
of the light curves and radial velocity time series to measure the mass,
radius, and orbital parameters of the candidate. We confirm and characterize HD
20329b, an ultra-short-period (USP) planet transiting a solar-type star. The
host star (HD 20329, $V = 8.74$ mag, $J = 7.5$ mag) is characterized by its G5
spectral type with $\mathrm{M}_\star= 0.90 \pm 0.05$ M$_\odot$,
$\mathrm{R}_\star = 1.13 \pm 0.02$ R$_\odot$, and $\mathrm{T}_{\mathrm{eff}} =
5596 \pm 50$ K; it is located at a distance $d= 63.68 \pm 0.29$ pc. By jointly
fitting the available TESS transit light curves and follow-up radial velocity
measurements, we find an orbital period of $0.9261 \pm (0.5\times 10^{-4})$
days, a planetary radius of $1.72 \pm 0.07$ $\mathrm{R}_\oplus$, and a mass of
$7.42 \pm 1.09$ $\mathrm{M}_\oplus$, implying a mean density of
$\rho_\mathrm{p} = 8.06 \pm 1.53$ g cm$^{-3}$. HD 20329b joins the $\sim$30
currently known USP planets with radius and Doppler mass measurements.
