We restudy the influence of beam wander on the uplink of ground-to-satellite laser communication, using the effective pointing error method, for a collimated untracked Gaussian beam under a weak atmospheric turbulence condition. It shows that the beam wander may cause significant increase in bit error rate (BER), and there exists an optimal transmitter radius for minimizing the value of BER. Further studies manifest that this optimal radius only changes with the laser wavelength and zenith angle, while independent on the satellite altitude and the fade threshold at the receiver. These results can be used in system design and optimization for the transmitter.