We 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 recompute and update the values for several system parameters of the triple system HU Vir (close and wide orbits). Spectroscopic observations were carried out with the STELLA echelle spectrograph (SES) at the robotic 1.2-m STELLA-I telescope at the Observatorio del Teide in Tenerife, Spain. A time series of 118 echelle spectra was taken in the period between Feb 17 to Jun 26, 2013. 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 RVs combined with the RV data available in the literature. Photometric observations were performed with the Amadeus Automatic Photoelectric Telescope (APT) at Fairborn Observatory in southern Arizona starting in 1996, 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.