The optical response of a Kronig-Penney type graphene superlattice is investigated. When an external field is applied along the periodicity of the superlattice, the total optical response of the graphene superlattice is enhanced due to the formation of anisotropic Dirac fermions. Such anisotropy tunes up the total optical spectra while maintaining the same critical electric field regardless of the degree of anisotropy. The optical conductance of anisotropic Dirac fermions exhibits two contrasting behaviours: (i) inversely proportional to the anisotropy and (ii) directly proportional to the anisotropy, depending on the direction of the external field. Interestingly, the anisotropy-induced optical conductance enhancement also occurs in gapped graphene with band structure anisotropy. This suggests that the enhanced electron-photon couplings in the presence of anisotropy is a general feature of the relativistic nature of the Dirac fermions in both massless and massive form. It is also revealed that the strong optical nonlinearity is a consequence of the relativistic nature of the Dirac fermions and the Dirac cone isotropy is not required. © 2012 IOP Publishing Ltd.