We study the structure of the upper mantle beneath Iceland using surface wave waveforms recorded at pairs of stations lying approximately on the same great circles as the sources used. We invert for local, path-average Vs variations between the station pairs. The method used in this study is an extension of an algorithm proposed by Kushnir et al. (1989), which uses only the phase of the seismograms. In our waveform inversion not only the phases but also the amplitudes of the surface waves are used as structural constraints. We illustrate the resolution power of the new algorithm with synthetic examples. We apply the method to study upper mantle structure beneath Iceland using recordings of three events with northerly, south-southwesterly and easterly orientated paths and 19 station pairs. Depending on the separation distance of the stations, we invert waveforms in the frequency range 0.0166-0.08 Hz and 0.01-0.08 Hz. Resolution is limited by the penetration depth of the surface wave fundamental mode, and is good down to ~150 km for the narrower frequency band and ~200 km for the wider band. Although the inversions of the differential waveforms only provide information on lateral Vs variations between station pairs, the main structural features of the upper mantle beneath Iceland are retrieved. We confirm that the strongest negative Vs anomalies of up to ~-5 per cent underlie central Iceland, and extend down to the limit of our resolution at ~200 km. The rift zones away from central Iceland are underlain by low velocities in the depth range ~50-100 km and high velocities below this, indicating that they are shallowly sourced. Such a structure also underlies northwest Vatnajokull, where a mantle plume is traditionally assumed to lie. Beneath intraplate areas, mantle structural variations are small. Using our method, smaller-scale mantle structures are detectable than is possible with teleseismic tomography, which tends to smear anomalies throughout larger volumes.