The Galactic center region provides a unique opportunity to determine the near- and mid-infrared extinction law, because bright sources are located behind a fairly uniform foreground screen extinction, thus avoding complications arising in situations of mixed emission/extinction as commonly found in star forming regions. From ISO-SWS observations of H recombination lines towards SgrA* we have found that the extinction law lacks the deep minimum in the 4-7um region that is expected for standard graphite/silicate mixes (see Fig.1). We propose to determine in more detail this unexpected shape of the extinction curve, and to check whether it applies to other lines of sight close to the center of our galaxy. Our observations will use as probes recombination lines of atomic hydrogen and groups of molecular hydrogen lines sharing a common upper level.