The beam wander and spot radius of sodium laser beacon (SLB) have direct effects on correction of adaptive optics. Based on wander variance and effective radius model of SLB, the differences in these aspects between SLB and laser are investigated under the three atmospheric turbulence models by the numerical simulation method. Then, the average effective radius of SLB spot for the long-exposure and short-exposure is calculated for different laser launch diameters. Effects of laser with repumping power on beam wander and spot radius of SLB are analyzed. Results show that the strength of atmospheric turbulence, laser launch diameters and the repumping power have influence on beam wander and spot radius of SLB.