We study the beam wander of a class of structured light beams, Hermite-Gaussian correlated Schell-model (HGCSM) beams, in theory and in experiment. It is found that modulating the coherence structure of a structured light beam can reduce the turbulence-induced beam wander, i.e., a HGCSM beam with larger mode orders or lower coherence experiences smaller beam wander. Our experimental results are consistent with theoretical predictions, and the insights here suggest that HGCSM beams could be useful in free-space optical communications.