  We propose a concrete form of a vertex function, which we call O-vertex, for
the intersection between an O5-plane and a 5-brane in the topological vertex
formalism, as an extension of the work of arXiv:1709.01928. Using the O-vertex
it is possible to compute the Nekrasov partition functions of 5d theories
realized on any 5-brane web diagrams with O5-planes. We apply our proposal to
5-brane webs with an O5-plane and compute the partition functions of pure
SO($N$) gauge theories and the pure $G_2$ gauge theory. The obtained results
agree with the results known in the literature. We also compute the partition
function of the pure SU(3) gauge theory with the Chern-Simons level $9$. At the
end we rewrite the O-vertex in a form of a vertex operator.
