The electrons in graphene exhibit unusual behaviours, which can be described by massless Dirac quasiparticles. Understanding electron scattering in graphene has been of significant importance for its future application in electronic devices because electron scattering determines electrical properties such as resistivity and electron transport. There are two types of electron scatterings in graphene: intervalley scattering and intravalley scattering. In single-layer graphene, to date, it has been difficult to observe intravalley scattering because of the suppression of backscattering resulting from the chiral nature of the electrons in graphene. Here, we report the multiple electron scattering behaviours in single-layer graphene on a metallic substrate. By applying one- and two-dimensional Fourier transforms to maps of the local density of states, we can distinguish individual scattering processes from complex interference patterns. These techniques enable us to provide direct evidence of intravalley scattering, revealing a linear dispersion relation with a Fermi velocity of ~7.4 × 10(5) m/s.