We present an analysis of the optical nuclear spectra from the active galactic nuclei (AGN) in a sample of giant low surface brightness (GLSB) galaxies. GLSB galaxies are extreme late type spirals that are large, isolated and poorly evolved compared to regular spiral galaxies. Earlier studies have indicated that their nuclei have relatively low mass black holes. Using data from the Sloan Digital Sky Survey (SDSS), we selected a sample of 30 GLSB galaxies that showed broad Hα emission lines in their AGN spectra. In some galaxies such as UGC 6284, the broad component of Hα is more related to outflows rather than the black hole. One galaxy (UGC 6614) showed two broad components in Hα, one associated with the black hole and the other associated with an outflow event. We derived the nuclear black hole (BH) masses of 29 galaxies from their broad Hα parameters. We find that the nuclear BH masses lie in the range 105 – 107 M⊙. The bulge stellar velocity dispersion σe was determined from the underlying stellar spectra. We compared our results with the existing BH mass - velocity dispersion (MBH–σe) correlations and found that the majority of our sample lie in the low BH mass regime and below the MBH–σe correlation. The effects of galaxy orientation in the measurement of σe and the increase of σe due to the effects of bar are probable reasons for the observed offset for some galaxies, but in many galaxies the offset is real. A possible explanation for the MBH–σe offset could be lack of mergers and accretion events in the history of these galaxies which leads to a lack of BH-bulge co-evolution.