  We propose 5-brane webs for 5d $\mathcal{N}=1$ $G_2$ gauge theories. From a
Higgsing of the $SO(7)$ gauge theory with a hypermultiplet in the spinor
representation, we construct two types of 5-brane web configurations for the
pure $G_2$ gauge theory using an O5-plane or an $\widetilde{\text{O5}}$-plane.
Adding flavors to the 5-brane web for the pure $G_2$ gauge theory is also
discussed. Based on the obtained 5-brane webs, we compute the partition
functions for the 5d $G_2$ gauge theories using the recently suggested
topological vertex formulation with an O5-plane, and we find agreement with
known results.
