Measuring surface differential rotation (DR) on different types of stars is important when characterizing the underlying stellar dynamo. It has been suggested that anti-solar DR laws can occur when strong meridional flows exist. We aim to investigate the differential surface rotation on the primary star of the RS CVn binary HU Vir by tracking its starspot distribution as a function of time. We also aim to recompute and update the values for several system parameters of the triple system HU Vir (close and wide orbits). Time-series high-resolution spectroscopy for four continuous months was obtained with the 1.2-m robotic STELLA telescope. Nine consecutive Doppler images were reconstructed from these data, using our line-profile inversion code iMap. An image cross-correlation method was applied to derive the surface differential-rotation law for HU Vir. New orbital elements for the close and the wide orbits were computed using our new STELLA radial velocities (RVs) combined with the RV data available in the literature. Photometric observations were performed with the Amadeus Automatic Photoelectric Telescope (APT), providing contemporaneous Johnson-Cousins $V$ and $I$ data for approximately 20 years. This data was used to determine the stellar rotation period and the active longitudes. We confirm anti-solar DR with a surface shear parameter $alpha$ of -0.029 $pm$ 0.005 and -0.026 $pm$ 0.009, using single-term and double-term differential rotation laws, respectively. The best fit is achieved assuming a solar-like double-term law with a lap time of $approx$ 400 d. Our orbital solutions result in a period of 10.387678 $pm$ 0.000003 days for the close orbit and 2726 $pm$ 7 d ($approx$ 7.5 yr) for the wide orbit. A Lomb-Scarge (L-S) periodogram of the pre-whitened $V$-band data reveals a strong single peak providing a rotation period of 10.391 $pm$ 0.008 d.
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