A simple method for frequency locking a frequency-doubled Nd:YAG laser to the center of line 1109 of the iodine absorption spectrum is described. The 31.6 GHz frequency shift provided by stimulated-Brillouin scattering from a single-mode silica fiber provides a probe signal that lies on the edge of line 1105 of the iodine spectrum. We adjust the frequency of the laser to maintain the transmission of a 5 cm iodine absorption cell at a value that places the unshifted laser line in the center of line 1109.