RX J0947.0+4721 is a newly discovered example of a narrow-line Seyfert 1 type object with a quasar level luminosity (M_B = -24.8). It was detected in the ROSAT All-Sky Survey (RASS) and later in 17 pointed observations of the ROSAT Position sensitive Proportional Counter (PSPC). The optical spectrum contains strong FeII emission. We apply several spectral models to the X-ray data. A single power law fit yields a photon index of -4.2. Single component thermal models underestimate the flux above 1 keV. A good fit is obtained with a blackbody plus power law model (photon index of 1.7 fixed) modified by Galactic absorption. The best fit temperature is T_bb= 108+-8 eV, and the flux ratio in the ROSAT band is f_bb/f_pl = 6. Large count rate variations are visible with a maximum amplitude of a factor > 17.5. The fastest change is a drop of a factor 2.7 in 25 hours. No spectral variations were observed. The maximum and minimum luminosities in the two component model are 1.0*10^46 ergs/s and < 6*10^44 ergs/s, respectively. We discuss possible explanations for the extreme softness and the observed variability.