  In this paper, we formulate a construction of ideal coset invariants for
surface-links in $4$-space using invariants for knots and links in $3$-space.
We apply the construction to the Kauffman bracket polynomial invariant and
obtain an invariant for surface-links called the Kauffman bracket ideal coset
invariant of surface-links. We also define a series of new invariants
$\{{\mathbf K}_{2n-1}(\mathcal L) | n=2, 3, 4, \ldots\}$ for surface-links
$\mathcal L$ by using skein relations, which are more effective than the
Kauffman bracket ideal coset invariant to distinguish given surface-links.
