  The $q$-deformation of the infinite-dimensional $n$-algebra is investigated.
Based on the structure of the $q$-deformed Virasoro-Witt algebra, we derive a
nontrivial $q$-deformed Virasoro-Witt $n$-algebra which is nothing but a
sh-$n$-Lie algebra. Furthermore in terms of the pseud-differential operators on
the quantum plane, we construct the (co)sine $n$-algebra and the $q$-deformed
$SDiff(T^2)$ $n$-algebra. We prove that they are the sh-$n$-Lie algebras for
the case of even $n$. An explicit physical realization of the (co)sine
$n$-algebra is given.
