Abstract: Fibre kinking is a failure mechanism of unidirectional carbon fibre-reinforced polymer (UD-CFRP) composites under longitudinal compression due to initial fibre misalignment. In view of this problem, macroscopic, microscopic and analytical methods have been proposed in the literature, but they all have certain limitations. Macroscopic models have poor prediction accuracy, microscopic models have high computational costs, analytical models can not be used on real geometries. In our previous work, a non-linear mean-field debonding model (NMFDM) was proposed to study non-linear effects of UD composites. The model considers not only the average asymmetric matrix plasticity (AAMP) but also the debonding failure of fibre-matrix interface. In this work, multi-scale simulations of kink band formation in UD composites were firstly investigated. Whereby a fibre kinking model was combined with the NMFDM for studying kink band formation of UD composites. The kink process of fibres under initial misalignment and the effect of different initial misalignment on stress and strain response were studied. The results show that the NMFDM can predict kind band formation on the multi-scale level in comparison with other numerical models and analytical models with the same accuracy but more efficiently.