  We present the complete structure of the nonlinear $N=2$ super extension of
Polyakov-Bershadsky, $W_3^{(2)}$, algebra with the generic central charge, $c$,
at the {\it quantum} level. It contains extra two pairs of fermionic currents
with integer spins 1 and 2, besides the currents of $N=2$ superconformal and
$W_3^{(2)}$ algebras. For $c\rightarrow \infty$ limit, the algebra reduces to
the classical one, which has been studied previously. The 'hybrid' field
realization of this algebra is also discussed.
