We report the discovery of a very H I-massive disc galaxy, HIZOA J0836-43, at a velocity of v(hel) = 10 689 km s(-1), corresponding to a distance of 148 Mpc (assuming H-0 = 75 km s(-1) Mpc(-1)). It was found during the course of a systematic H I survey of the southern Zone of Avoidance (ZOA) (|b| <= 5 degrees) with the multibeam system at the 64-m Parkes radio telescope. Follow-up observations with the Australia Telescope Compact Array reveal an extended H I disc. We derive an H I mass of 7.5 x 10(10) M-circle dot. Using the H I radius, we estimate a total dynamical mass of 1.4 x 10(12) M-circle dot, similar to the most massive known disc galaxies such as Malin 1. HIZOA J0836-43 lies deep in the ZOA (l, b = 262.degrees 48, -1.degrees 64) where the optical extinction is very high, A(B) = 9.8 mag. However, in the near-infrared (NIR) wavebands, where the extinction is considerably lower, HIZOA J0836-43 is clearly detected by both the Deep Near Infrared Survey of the Southern Sky (DENIS) and Two-Micron All-Sky Survey (2MASS). Deep Anglo-Australian Telescope NIR (K-s and H band) images show that HIZOA J0836-43 is an inclined disc galaxy with a prominent bulge (scalelength 2.5 arcsec or 1.7 kpc), and an extended disc (scalelength 7 arcsec or 4.7 kpc) which can be traced along the major axis out to a radius of 20 arcsec or 13.4 kpc (at 20 mag arcsec(-2) in K-s). The H I disc is much more extended, having a radius of 66 kpc at 1 M-circle dot pc(-2). Detections in the radio continuum at 1.4 GHz and at 60 mu m (IRAS) are consistent with HIZOA J0836-43 forming stars at a rate of similar to 35 M-circle dot yr(-1). We compare the properties of HIZOA J0836-43 with those of the most H I-massive galaxies currently known, UGC 4288, UGC 1752 and Malin 1, all of which are classified as giant low surface brightness galaxies.