A thermo-mechanical finite element simulation is developed for additive manufacturing by directed energy deposition (DED). The simulation is conducted at the scale of the part, by modelling the progressive deposition of matter and the energy source by the way of fraction of layer. To incrementally resolve the displacement, strain and stress fields, a theoretical formulation for the kinematic positioning is proposed to minimize the distortion of the non-constructed fraction by considering current displacement and strain in the constructed part, which can resolve the discontinuous problem at interface for a patch of material deposition. Moreover, it is found that the kinematic hardening couldn’t be ignored for the back-and-forth deposition mode of DED process, its effects on final distortion and residual stress are studied. The validation of the developed model is obtained by comparison with experimental results taken from the literature for the case of a turbine blade showing a strong curvature.