A dispersion analysis of Rg waves generated by local earthquakes surrounding the Alboran Sea (Western Mediterranean) has been undertaken to obtain its shear-wave velocity structure at shallow depths. We have used single-component short-period stations belonging to the Regional Seismic Network of Andalucia and the Spanish National Seismic Network. Our database includes seismograms generated by 18 earthquakes that occurred in the area during the period of 1992–95. The seismic events, with magnitudes between 2.9 and 4.9 and focal depths ranging from 2.7 to 12 km, were recorded at 13 stations at distances between 91 and 245 km from the source. We have analysed a total of 20 source-station Rg-wave paths. These seismic trajectories across the Alboran Sea provide irregular path coverage due to their geographical location. Despite sparse sampling the data collected have been processed with the help of digital filtering and group velocity dispersion curves have been obtained. The path group velocities vary from 1.21 to 1.91 km s⁻¹ within the 1.7–5.8 s period interval. Then using a generalised inversion approach we have obtained 1D shear-wave velocity models for all source-station paths. Inversion for shear velocity structure gives velocity profiles down to a depth of 5 km. The shear-wave velocities range between 0.7 and 3.2 km s⁻¹ within the standard deviation band of 0.05–0.17 km s⁻¹, and show significant variations from each other in the region of the Alboran Basin. We have applied an imaging technique aimed at volumetric modelling and data visualisation and we hereby present the tomographic results based on ray-path seismic velocities that were obtained for the basin. We have got an overall view of the sedimentary cover of the area regarding its geometry and S-wave velocity structure at very shallow depths (0–5 km). Although the relationship between lateral change in Rg dispersion and geologic structure may not be straightforward, we have observed a good correlation between those changes and surface geology.