A galactose oxidase gene, gao-5f, was cloned from Fusarium odoratissimum and successfully expressed in E. coli. The galactose oxidase GAO-5F belongs to the AA5 family and consists of 681 amino acids, with an estimated molecular weight of 72 kDa. GAO-5F exhibited maximum activity at 40 °C and pH 7.0 and showed no change in activity after 24 h incubation at 30 °C. Moreover, GAO-5F exhibited 40% of its maximum activity after 24 h incubation at 50 °C and 60% after 40 h incubation at pH 7.0. The measured thermostability of GAO-5F is superior to galactose oxidase’s reported thermostability. The enzyme exhibited strict substrate specificity toward D-galactose and oligosaccharides/polysaccharides containing D-galactose. Further analysis demonstrated that GAO-5F specifically oxidized agarose to a polyaldehyde-based polymer, which could be used as a polyaldehyde to crosslink with gelatin to form edible packaging films. To our knowledge, this is the first report about the modification of agarose by galactose oxidase, and this result has laid a foundation for the further development of edible membranes using agarose.