The masses of the most massive supermassive black holes (SMBHs) predicted by the M_BH-sigma and M_BH-luminosity relations appear to be in conflict. Which of the two relations is the more fundamental one remains an open question. NGC 1332 is an excellent example that represents the regime of conflict. It is a massive lenticular galaxy which has a bulge with a high velocity dispersion sigma of ~320 km/s; bulge–disc decomposition suggests that only 44% of the total light comes from the bulge. The M_BH-sigma and the M_BH-luminosity predictions for the central black hole mass of NGC 1332 differ by almost an order of magnitude. We present a stellar dynamical measurement of the SMBH mass using an axisymmetric orbit superposition method. Our SINFONI integral-field unit (IFU) observations of NGC 1332 resolve the SMBH’s sphere of influence which has a diameter of ~0.76 arcsec. The sigma inside 0.2 arcsec reaches ~400 km/s. The IFU data allow us to increase the statistical significance of our results by modelling each of the four quadrants separately. We measure a SMBH mass of (1.45 \pm 0.20) x 10^9 M_sun with a bulge mass-to-light ratio of 7.08 \pm 0.39 in the R-band. With this mass, the SMBH of NGC 1332 is offset from the M_BH-luminosity relation by a full order of magnitude but is consistent with the M_BH-sigma relation.