The oscillatory quantum screening effects on the positronium formation by the positron are investigated in quantum plasmas. It is found that the oscillatory screening effects suppress the positronium formation radius as well as the positronium formation cross section. It is also found that the positronium formation radius decreases with increasing quantum wave number. It is found that the peak position of the differential cross section is receded from the projectile with decreasing quantum wave number. In addition, the oscillatory screening effects on the positronium formation cross section are found to be decreased with an increase of the collision energy.