This paper performs the seismic assessment of novel SMA-based self-centring (SC) eccentrically braced frames (EBFs) by using probability seismic demand analysis (PSDA) and probability seismic fragility analysis (PSFA). The structural finite element models are established based on a previous prototype building and verified through test results. The PSDA is based on a set of 176 seismic records, and Saavg is chosen as the proper intensity measure (IM) for max inter-storey drift ratio (MIDR) and max inter-storey residual drift ratio (MIRR); whereas PGA is more suitable for peak floor acceleration (PFA). After the PSDA results are obtained, time-history analyses and PSFA are conducted. Compared with traditional steel EBFs, the SMA-based SC-EBF shows a slight weakness in MIDR due to the comparatively small energy dissipation capacity but has an apparent advantage in controlling MIRR due to a good SC capacity provided by SMA angles. Furthermore, although the steel EBF with fixed column bases has the smallest MIDR, the fixed bases will cause extra damage in column bases, which will bring other problems in post-seismic rebuild and deviate from the design target of concentrating damage in link beams. The variable of the PFA is small, showing that the influence of structural forms on PFA is not apparent. Considering the overall structural seismic performances in terms of MIDR, MIRR and PFA, SMA-based SC-EBF can be a promising alternative in future seismic-resistant designs.