We propose an extended form of the topological vertex formalism that applies to (p,q)-brane web with orientifolds, which realizes five dimensional SO(N) gauge theories in the string theory. A new topological vertex with only one leg is introduced into the formalism for the intersection point of (2,1)-brane and the O-plane. We show the consistency of this extended formalism and present the resulted analytic expression for the partition function of SO(N) gauge theories etc.