We investigate the features of additional waves that arise in the graphene layered medium, within the framework of nonlocal effective medium model. The additional wave is manifest on the biquadratic dispersion relation of the medium and represents as a distinctive nonlocal character at long wavelength. In particular, the reflection and transmission coefficients for the nonlocal medium are underdetermined by Maxwell's boundary conditions. An additional boundary condition based on modal expansions is proposed to derive the generalized Fresnel equations, based on which the additional wave in the graphene layered medium is determined. The additional wave tends to be significant near the effective plasma frequency, near which the graphene plasmons are excited inside the medium. (C) 2014 Optical Society of America