First multi-colour complete light curves and low-resolution spectra of short-period eclipsing binary TT Cet are presented. The stellar atmospheric parameters of the primary star were derived through spectra fitting as: T-eff = 7 091 +/- 124 K, log g = 4.15 +/- 0.33 cm/s(2), and [Fe/H]=-0.23 +/- 0.04 dex. The light curves were analysed using the Wilson-Devinney code. The photometric solution suggests that this target should be a near-contact binary with the primary component filling its critical Roche lobe (i.e. SD1-type NCB). The luminosity enhancement around the primary light maximum (phase 0.10-0.40) on the light curve was detected like other SD1-type NCBs, which could be caused by a hot spot near the facing surface of the secondary component due to mass transfer. Long-term decrease of the orbital period at a rate of dP/dt=-5.01 (+/- 0.06) x 10(-8) d center dot yr(-1) was detected by the O-C analysis, which supports the mass transfer from the primary to the secondary and is consistent with its primary filling configuration. No third body was found through the light curve and O-C analysis. TT Cet may locate in the broken contact stage predicted by the thermal relaxation oscillation theory (TRO) and will evolve to the contact stage eventually. It is another good observational example supporting the TRO theory. We have collected all known SD1-type NCBs with absolute parameters from the literatures. The relations of these parameters are summarised for these rare systems.