Preterm infants are vulnerable to the oxidative stress due to the production of large amounts of free radicals, antioxidant system insufficiency, and immature oligodendroglial cells. Reactive oxygen species (ROS) play a pivotal role in the development of periventricular leukomalacia. The three most common ROS are superoxide ($O2^{cdot-}$), hydroxyl radical ($OH^{cdot}$), and hydrogen peroxide ($H_2O_2$). Under normal physiological conditions, a balance is maintained between the production of ROS and the capacity of the antioxidant enzyme system. However, if this balance breaks down, ROS can exert toxic effects. Superoxide dismutase, glutathione peroxidase, and catalase are considered the classical antioxidant enzymes. A recently discovered antioxidant enzyme family, peroxiredoxin (Prdx), is also an important scavenger of free radicals. Prdx1 expression is induced at birth, whereas Prdx2 is constitutively expressed, and Prdx6 expression is consistent with the classical antioxidant enzymes. Several antioxidant substances have been studied as potential therapeutic agents; however, further preclinical and clinical studies are required before allowing clinical application.