X-ray variability in the 0.1–2.4 keV ROSAT energy band with a doubling timescale of 800 s and a factor of 4 within a few hours has been detected in a 20 ksec pointing on the IRAS AGN 13224-3809. The optical spectrum indicates that IRAS 13224-3809 is a narrow-line Seyfert 1 galaxy with strong permitted Fe II emission, a member of the unusual I Zw 1 class objects. IRAS 13224-3809 appears to be one of the most rapidly variable AGN known so far. This is the first time that variability on a timescale smaller than 1000 s is reported at such high L (0.1–2.4 keV) = 3·1044erg · s−1 X-ray luminosity 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 H I wings can be explained if only 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 H I lines in IRAS 13224-3809.