Summary: A Hom-structure on a Lie algebra \((\mathfrak{g},[\cdot,\cdot])\) is a linear map \(\sigma:\mathfrak{g}\to\mathfrak{g}\) which satisfies the Hom-Jacobi identity \[ [[x,y],\sigma(z)]+[[z,x],\sigma(y)]+[[y,z],\sigma(x)]=0 \] for all \(x,y,z\in\mathfrak{g} \). A Hom-structure is called regular if \(\sigma\) is also a Lie algebra isomorphism. Let \(\mathcal{N}\) be the Lie algebra consisting of all strictly upper triangular \((n+1)\times(n+1)\) matrices over a field \(\mathbb{F} \). In this paper, we prove that if \(n\geq 4\), any regular Hom-structure \(\sigma\) on \(\mathcal{N}\) is a product of a special inner automorphism, an extremal inner automorphism and a central automorphism of \(\mathcal{N} \). As its application, the set of all regular Hom-structures on \(\mathcal{N}\) forms a normal subgroup of the automorphism group of \(\mathcal{N} \).