Summary: For the simple Lie algebra \(\mathfrak{so}_m\), we study the commutant vertex operator algebra of \(L_{\widehat{\mathfrak{so}}_{m}}(n,0)\) in the \(n\)-fold tensor product \( L_{\widehat{\mathfrak{so}}_{m}}(1,0)^{\otimes n}\). It turns out that this commutant vertex operator algebra can be realized as a fixed point subalgebra of \(L_{\widehat{\mathfrak{so}}_{n}}(m,0)\) (or its simple current extension) associated with a certain abelian group. This result may be viewed as a version of level-rank duality.