X-ray variability in the 0.1 – 2.4 keV ROSAT energy band with a doubling time scale of 800 s and a factor of 4 within a few hours has been detected in a 20 ksec pointing on the AGN IRAS 13224-3809. The optical spectrum indicates that IRAS 13224-3809 is a narrow-line Seyfert 1 galaxy with strong permitted Fell emission, a member of the unusual I Zw 1 class objects. IRAS 13224-3809 appears to be the most rapidly varying AGN known so far. This is the first time that variability on a time scale smaller than 1000 s is reported at such high X-ray luminosity [L(0.1 − 2.4 keV) = 3 · 1044 erg s−1] in Seyfert galaxies. It is also the first reported X-ray variability in I Zw 1 class objects. The Δt = 800 s variation indicates that the X-rays come from a compact region of about 17 light minutes in size. Our results from the X-ray spectral analysis favour a scenario in which a hard X-ray source irradiates the accretion disk which reemits at soft X-ray energies. The absence of broad HI wings can be explained only if a part of the BLR, far from the centre, is observed and the bulk of the region, which emits the wings, is hidden. We want to draw attention to the fact that rapid X-ray variability could also be connected with the absence of broad HI lines in IRAS 13224-3809.