The seismic velocity structure of the Granada Basin (southern Spain) at depths of 1-4 km is investigated by dispersion analysis of 0.5- to 5.9-sec Rayleigh waves. We have used records from 12 quarry blasts detonated between 1990 and 2000 and 16 local earthquakes with magnitudes between 2.6 and 3.8 that occurred between 1990 and 1997. All events were recorded on the Regional Seismic Network of Andalucia, Spain, and on the National Seismic Network. P-, S- and Rg-phases were recorded at 13 stations at distances between 10 and 72 km from the source. The analysis and inversion of Rg waveforms is performed using multiple filtering techniques and a generalized inversion approach. We measured ray-path group velocities from 0.83 to 2.15 km/sec in the 0.6- to 5.8-sec period interval, and obtained shear-wave velocity profiles for 29 source-station paths. The shear velocities lie between 0.8 and 3.34 km/sec within a standard deviation band of 0.05-0.14 km/sec. From these models, it is possible to infer the most conspicuous features in the upper 4 km of the region and the existence of some degree of lateral variation in velocity. After applying an imaging method aimed at volumetric modeling and data visualization, we present the first velocity images obtained for the Granada Basin. Our results characterize the basin and are correlated with the surface geology.