The seismic response of reinforced concrete (RC) plan-asymmetric structures is significantly influenced by the input angle of seismic ground motions. Hence, it is challenging to assess the performance of plan-asymmetric structures. In this study, the classic probabilistic seismic fragility assessment method is used to assess RC plan-asymmetric wall-frame structures based on the enhanced damage model. First, the worst-case input angle of seismic ground motions for plan-asymmetric structures is identified using the wavelet transforms coefficient method, considering the coupling of bidirectional seismic ground motions. Accordingly, the maximum deformation and hysteretic energy dissipation can be determined. Then, an enhanced damage model, which is based on the combination of deformation and hysteretic energy dissipation, is used to identify floor damage factor. Note that the importance coefficients of structural components are considered in the identification. Meanwhile, the incremental dynamic analysis (IDA) is conducted to create the fragility curves by assuming floor damage factor as seismic performance index. In particular, the randomness of the threshold for floor damage factor is considered during the assessment. Afterwards, numerical simulations are employed to verify the fragility assessment method. Results show that the wavelet transforms coefficient method can evaluate the worst-case input angles with low time-consuming and high efficiency. Meanwhile, the story damage factors confirmed that the proposed damage model could accurately assess the structure during the failure process. Moreover, the typical failure modes of the RC wall-frame structure, which significantly depend on the story damage distribution, can be defined using the enhanced damage model. Note that the randomness of the threshold could significantly affect the probability of exceedance, which is important for fragility analysis.