To explore the practicability of elect ronics based on graphene superlattice (GSL),using the transfer matrix method,the properties of electronic band gap and transport in period-doubling quasi-peri odic graphene superlattice have been investigated.It is found that such a struct ure cn posses a zero- gap which exists in high period-doubling sequences.Different from Bragg gap,the position of the zer o - gap associated with Dirac point is less sensitive to the incidence angle and lattice constants.Furthermore,we investigate the incident angle on the electronic transport and the distribution of the allowed bandwidths for high generations.which gives a good insight about their power laws.The characteristics of electron transport over period-doublin g graphene superlattice may facilitate the development of many graphene-based e lectronics devices.