We revisit the free field construction of the deformed $W$-algebra by Frenkel
and Reshetikhin,{\it Commun.\ Math.\ Phys.\ }{\bf 197}, 1-31 (1998),where the
basic $W$-current has been identified. Herein, we establish a free field
construction of higher $W$-currents of the deformed $W$-algebra associated with
the twisted affine Lie algebra $A_{2N}^{(2)}$. We {obtain} a closed set of
quadratic relations and duality, which allows us to define deformed $W$-algebra
${\cal W}_{x,r}\big(A_{2N}^{(2)}\big)$ using generators and relations.
