The process parameters of laser additive manufacturing have an important influence on the forming quality of the produced items or parts. In the present work, a finite element model for simulating transient heat transfer in such processes has been implemented using the ANSYS software, and the temperature and stress distributions related to 316L stainless steel thin-walled ring parts have been simulated and analyzed. The effect of the laser power, scanning speed, and scanning mode on temperature distribution, molten pool structure, deformation, and stress field has been studied. The simulation results show that the peak temperature, weld pool size, deformation, and residual stress increase with an increase in laser power and a decrease in the scanning speed. The scanning mode has no obvious effect on temperature distribution, deformation, and residual stress. In addition, a forming experiment was carried out. The experimental results show that the samples prepared by laser power P = 800 W, V = 6 mm/s, and the normal scanning method display good quality, whereas the samples prepared under other parameters have obvious defects. The experimental findings are consistent with the simulation results.