We continue the study of the vertex operator algebra L(k,0) associated to a
type G2(1)β affine Lie algebra at admissible one-third integer levels, k=β2+m+3iβΒ (mβZβ₯0β,i=1,2), initiated in
\cite{AL}. Our main result is that there is a finite number of irreducible
L(k,0)-modules from the category O. The proof relies on the
knowledge of an explicit formula for the singular vectors. After obtaining this
formula, we are able to show that there are only finitely many irreducible
A(L(k,0))-modules form the category O. The main result then
follows from the bijective correspondence in A(V)-theory.Comment: 28 pages, 1 tabl