Microstructure control is a great challenge for selective laser melting (SLM) mainly because of nonuniform and ultra-rapid heating and cooling in the process. It is related to the control of dendrite morphology evolution and competitive grain growth by adjusting the process parameters of SLM. In this study, a multiscale simulation approach, which combines the finite element method (FEM) and the phase field (PF) method, is performed to investigate the dendrite morphology and stray grain growth under various SLM parameters for Inconel 718 superalloy. The cooling characteristics of melt pool, including the cooling rate, thermal gradient/solidification ratio (G/R), and the slope of the solidification front are investigated. Meanwhile, experiment verification adopting the manufacturing parameters identical to the simulation is performed. It is shown that simultaneously increasing or decreasing the laser power and scan speed leads to a drastic change of melt pool aspect ratio (MPAR), and this in turn affects the competitive growth of stray grains. Overall, a larger MPAR is found to suppress the growth of stray grains more effectively. Also, the experimental results are found to agree well with the simulation results. Three mechanisms of stray grain growth are revealed from the simulation results, and their roles are analzyed. This study provides important insights into the microstructure control in the laser additive manufacturing processes.