The blind source separation theory was introduced and the trend and amplitude (TAA) model was established in order to overcome the shortcomings of some traditional global leakage discharge analysis models in water distribution systems (WDS). The TAA model considers the leakage discharge as one part of the total water supply flow, consisting of constrained independent component analysis (CICA) model and amplitude solving model. In the CICA model, the CICA algorithm was chosen and two reference vectors were constructed, and then the trend of leakage discharge was obtained. In the amplitude solving model, the two-element coupled linear overdetermined equations were derived and the amplitude was calculated. The TAA model was optimized and verified based on the data from three kinds of WDS (the laboratory WDS, the emulational WDS and the actual WDS). The simulation accuracy of the TAA model was high enough when the total water supply flow was a non-Gaussian signal in the WDS with one entrance only; the TAA model can effectively avoid the complexity (and reflect the uncertainty) of the relationship between leakage discharge and pressure head. More importantly, the model has good transplant performance.