  Electronic band gap and transport in quasi-periodic graphene superlattice of
double-periodic sequence have been investigated. It is found that such
quasi-periodic structure can possess a zero-averaged wave number
(zero-$\bar{k}$) gap which associated with an unusual Dirac point. Different
from Bragg gap, the zero-$\bar{k}$ gap is less sensitive to the incidence
angle, and robust against the lattice constants. The locations of Dirac point
and multi-Dirac-points in the graphene superlattices of various sequences are
also compared. The control of electron transport over the zero-$\bar{k}$ band
gap in graphene superlattice may facilitate the development of many
graphene-based electronics.
