In the present work, we consider the electronic properties of graphene with Kekule structure formed from two different C–C bonds in its hexagonal lattice. When the C–C bond alternation was introduced, a small band gap has been opened in the band structure of graphene and it increases linearly by a difference in the bond lengths δ. While the applied strain along the zigzag or armchair direction causes band gap to decrease rapidly to zero, the strain in the other directions can increase the band gap. Interestingly, when the graphene with Kekule structure is strained, its band gap is inversely proportional to the bond length difference δ. Opening a band gap in graphene due to bond alternation and strain can open up new applications in nanoelectronic devices.