The forming capability and post-forming quality of metal parts in laser additive manufacturing processes are directly dependent on the choice of process parameters. In order to study the effects of laser process parameters on the temperature and stress fields of additive components, numerical simulation is performed for the single-pass deposition process of GH4169 powder on 304L substrate based on thermo-mechanical sequential coupled finite element method in this paper. The effects of laser power and scanning speed on temperature field and residual stress are investigated in depth on the basis of the experimentally validated numerical model, and the relationship between stress field and temperature field is explored. Both increasing laser power and decreasing scanning speed obviously reduce the temperature gradient during the cooling phase of the deposited layer and substrate near the edge of the deposited layer, and the temperature gradient is proportional to the transverse and longitudinal residual stresses in this region. In the deposition layer, the change of scanning speed has little effect on the transverse and longitudinal temperature gradient and residual stresses. Increasing the laser power makes the longitudinal temperature gradient in this area significantly lower, but leads to a slight increase of transverse and longitudinal residual stresses, which implies that there is no distinct proportional relationship between the residual stress and the temperature gradient in this region.