  We propose new topological vertex formalism for Type IIB $(p,q)$ 5-brane web
with an O5-plane. We apply our proposal to 5d $\mathcal{N}=1$ Sp(1) gauge
theory with $N_f=0,1,8$ flavors to compute the topological string partition
functions and check the agreement with the known results. Especially for the
$N_f=8$ case, which corresponds to E-string theory on a circle, we obtain a
new, yet simple, expression of the partition function with two Young diagram
sum.
