Vehicle velocity and side-slip angle are important vehicle states for the electronic stability programme and traction control system in vehicle safety control system and for the control allocation method of electric vehicles with in-wheel motors. This paper proposes an innovative side-slip angle estimator based on the non-linear Dugoff tyre model and non-singular terminal sliding mode observer. The proposed estimation method based on the non-linear tyre model can accurately present the tyre's non-linear characteristics and can show advantages over estimation methods based on the linear tyre model. The utilised Dugoff tyre model has a relatively simple structure with few parameters, and the proposed non-linear observer can be applied in various vehicle tyres and various road conditions. Precise determination of the Dugoff tyre model parameters is not required and the proposed observer can still perform good estimation results even though tyre parameters and the tyre-road friction coefficient are not accurate. The proposed non-singular terminal sliding mode observer can achieve fast convergence rate and better estimation performance than the traditional sliding mode observer. At the end of this paper, simulations in various conditions are presented to validate the proposed non-linear estimator.