A waveform inversion method is applied to 156 Love and Rayleigh wave seismograms to build up a 3-D model of the shear velocity in the upper mantle beneath the Indian Ocean. The first step of the method consists in finding, for each path, a radially stratified upper mantle model compatible with the Love and Rayleigh wave seismograms relative to that path. The fundamental mode and few higher modes are modelled in the waveform inversion. In a second step, the models related to the different paths are used in a tomographic inversion to map the 3-D upper mantle structure. The 3-D velocity model has a lateral resolution of 1000 km. No significant velocity anomalies are found below 300 km, although the resolution is still good. Continental roots are confined to the upper 300 km and low velocities below mid-oceanic ridges to the upper 250 km, depending on their spreading rates. At shallow depths (<80 km), we find a positive velocity anomaly beneath the West Indian ridge near the Rodriguez triple junction, where gravimetric and bathymetric data indicate a reduced volcanic activity. At greater depth (around 200 km), a low velocity signature is found beneath the hot-spot of R¿union-Mauritius islands and the Central Indian ridge. It could reflect a real connection between the two structures.¿ 1997 American Geophysical Union