  We investigate the $Spin(7)$ holonomy metric of cohomogeneity one with the
principal orbit $SU(3)/U(1)$. A choice of U(1) in the two dimensional Cartan
subalgebra is left as free and this allows manifest $\Sigma_3=W(SU(3))$ (= the
Weyl group) symmetric formulation. We find asymptotically locally conical (ALC)
metrics as octonionic gravitational instantons. These ALC metrics have orbifold
singularities in general, but a particular choice of the U(1) subgroup gives a
new regular metric of $Spin(7)$ holonomy. Complex projective space ${\bf
CP}(2)$ that is a supersymmetric four-cycle appears as a singular orbit. A
perturbative analysis of the solution near the singular orbit shows an evidence
of a more general family of ALC solutions. The global topology of the manifold
depends on a choice of the U(1) subgroup. We also obtain an $L^2$-normalisable
harmonic 4-form in the background of the ALC metric.
