The Tau Inversion method has been used to invert earthquake travel times from the Hawaiian Ridge to determine velocity structure with limits. The inversion gives a velocity model showing a rapid increase in velocity from 5.9 km/sec to 7.2 km/sec between 4-km and 7.5 -km depth, a monotonic increase to 7.5 km/sec near 11 km, and Moho velocity of 8.0 km/sec at 15 -km depth. Three prominent travel time delays, indicating heterogeneous velocity structure, are shown to correspond to the major volcanoes on Hawaii: Kilauea, Mauna Loa and Mauna Kea. Also, from the Moho depth determined by Tau Inversion, we infer that previous estimates of crustal flexure for the Hawaiian Ridge, based on deeper Moho depths (>15 km), are too large. The Tau method is shown to be useful in delineating heterogeneous velocity structure and determining limits on velocity depth models from local earthquake travel time data.