Glutathione (GSH) is an important antioxidant in plants, animals, fungi, and some bacteria and archaea. But i want to know why does it has an unusual peptide link and what are its effects?
You are right. Glutathione has a peculiar bond between glutamic acid and cysteine residues. The link occurs through γ-carboxyl group of glutamate instead of the (expected) α-carboxyl group. As a consequence, common peptidases are unable to hydrolyze the bond. Few enzymes are able to break it, such as γ-glutamyltranspeptidase (GGT).
Take a look at:
Lu, S. C. (2013). Glutathione synthesis. Biochimica Et Biophysica Acta, 1830(5), 3143–3153. http://doi.org/10.1016/j.bbagen.2012.09.008
Glutathione a tripeptide, is one of the major natural antioxidant in the body, I believe the reason for the unusual peptide bond formation is to prolong it's lifespan in the body. This is in addition to Daniel's earlier comment.