We present a catalogue of an HI-selected sample of 1129 low surface brightness galaxies (LSBGs) searched from the {alpha}.40-SDSS DR7 survey. This sample, consisting of various types of galaxies in terms of luminosity and morphology, has extended the parameter space covered by the existing LSBG samples. Based on a subsample of 173 LSBGs that are selected from our entire LSBG sample to have the 2-horn shapes of the HI line profiles, minor-to-major axial ratios (b/a) less than 0.6 and signal-to-noise ratio of HI detection greater than 6.5, we investigated the Tully-Fisher relation (TFr) of LSBGs in the optical B, g, and r bands and near-infrared (NIR) J, H, and K bands as well. In optical bands, the LSBG subsample follows the fundamental TFr that was previously defined for normal spiral galaxies. In NIR bands, the TFrs for our LSBG subsample are slightly different from the TFrs for the normal bright galaxies. This might be due to the internal extinction issue. Furthermore, the mass-to-light ratio (M/L), disc scale length (h), and mass surface density ({sigma}) for our LSBG subsample were deduced from the optical TFr results. Compared with high surface brightness galaxies (HSBGs), our LSBGs have higher M/L, larger h, and lower {sigma} than HSBGs.