The University of Tasmania Mt Pleasant 26-m and Ceduna 30-m radio telescopes have been used to search for 6.7-GHz class II methanol masers towards 200 GLIMPSE (The Galactic Legacy Infrared Mid-Plane Survey Extraordinaire) sources. The target regions were selected on the basis of their mid-infrared colours as being likely to be young high-mass star formation regions and are either bright at 8.0{mu}m, or have extreme [3.6]-[4.5] colour. Methanol masers were detected towards 38 sites, nine of these being new detections. The prediction was that approximately 20 new 6.7-GHz methanol masers would be detected within 3.5-arcmin of the target GLIMPSE sources, but this is the case for only six of the new detections. A number of possible reasons for the discrepancy between the predicted and actual number of new detections have been investigated. It was not possible to draw any firm conclusions as to the cause, but it may be because many of the target sources are at an evolutionary phase prior to that associated with 6.7-GHz methanol masers. Through comparison of the spectra collected as part of this search with those in the literature, the average lifetime of individual 6.7-GHz methanol maser spectral features is estimated to be around 150yr, much longer than is observed for 22-GHz water masers.