Rayleigh wave group velocity dispersion has been used to study the lithospheric structure along the Walvis Ridge and for a nearby South Atlantic path. Group velocity is anomalously low in the period range of 15--50 s for both surface wave paths. Results of a formal inversion for the ridge suggest crustal thickening to 12.5 km and anomalously low mantle shear velocity of 4.25--4.35 km/s to depths of 45 km. Lowering the density in this region during inversion does not raise the shear velocity to the oceanic norm. A nearby off-ridge path that covers the Cape Basin and part of the western Walvis Ridge shows no sign of thickened crust. No significant differences from normal oceanic lithosphere exist below 50 km, and no signs of thinning of the lithosphere under the Walvis Ridge are apparent. Other geophysical data rule out a thermal cause for the low mantle shear velocity, and it is likely that unusual mantle composition is responsible.