Despite the importance of high-impedance fault (HIF) modelling as a key issue in numerous power system studies, there is no single model accurately representing the behaviour of each type of HIFs. Tree-related HIF (THIF) is a complex type that occurs when a power line comes in contact with a live tree. Given that available models for HIF cannot represent the expected behaviour of a live THIF, the need for a more accurate model seems obvious. So, in this study, based on experimental data obtained from measurements, the effective factors in HIF caused by live trees are studied and a new mathematical model of THIF provided in order to present the effects of both environmental conditions and biological classification. This model represents low and high frequency behaviours of THIFs, which are, respectively, derived in block-oriented feed-forward form and sinusoidal functions. Moreover, this study proposes a hybrid technique based on the combination of kernel density estimation and wavelet analysis to perform a feature extraction from THIF signals.