  The Lie superalgebra $\mathfrak{psl}(2|2)$ is recognized as a pretty special
one in both mathematics and theoretical physics. In this paper, we present the
Drinfeld realization of the Yangian algebra associated with the centrally
extended Lie superalgebra $\mathfrak{psl}(2|2)$. Furthermore, we show that it
possesses the Hopf algebra structures, particularly the coproducts. The idea to
prove the existence of the manifest coproducts is the following. Firstly, we
shall introduce them to Levendorskii's realization, a system of a finite
truncation of the Drinfeld generators. Secondly, we show that Levendorskii's
realization is isomorphic to the Drinfeld realization by induction.
