From CCD observations carried out with different telescopes, we present short-term photometric measurements of the large trans-Neptunian object Varuna in 10 epochs, spanning around 19 years. We observe that the amplitude of the rotational light curve has changed considerably during this period of time from 0.41 to 0.55 mag. In order to explain this variation, we constructed a model in which Varuna has a simple triaxial shape, assuming that the main effect comes from the change of the aspect angle as seen from Earth, due to Varuna’s orbital motion in the 19 year time span. The best fits to the data correspond to a family of solutions with axial ratios b/a between 0.56 and 0.60. This constrains the pole orientation in two different ranges of solutions presented here as maps. Apart from the remarkable variation of the amplitude, we have detected changes in the overall shape of the rotational light curve over shorter timescales. After the analysis of the periodogram of the residuals to a 6.343572 hr double-peaked rotational light-curve fit, we find a clear additional periodicity. We propose that these changes in the rotational light-curve shape are due to a large and close-in satellite whose rotation induces the additional periodicity. The peak-to-valley amplitude of this oscillation is in the order of 0.04 mag. We estimate that the satellite orbits Varuna with a period of 11.9819 hr (or 23.9638 hr), assuming that the satellite is tidally locked, at a distance of ̃1300 km (or ̃2000 km) from Varuna, outside the Roche limit.