From the marine refraction data recorded on five instruments during the Clipperton Area Seismic Survey to Investigate Compensation (CLASSIC) experiment in 1994 we construct a compressional velocity model for a 108 km long profile across the Clipperton transform. We apply a new seismic tomography code that alternates between ray tracing and linearized inversions to find a smooth seismic velocity model that fits the observed refraction travel times. The solution to the forward ray-tracing problem is a hybrid of the graph (or shortest path) method and a ray-bending method. The inversion is performed with least squares penalties on the data misfit and first derivatives of the seismic structure. Starting with a one-dimensional compressional velocity model for oceanic crust, the misfit in the normalized travel time residuals is reduced by 96%, decreasing the median travel time residual from 110 to 25 ms. The compressional velocity structure of the Clipperton transform is characterized by anomalously low velocities, about 1.0 km/s lower than average, beneath the median ridge and parallel troughs of the transform domain. The low compressional velocities can be explained by an increased porosity due to fracturing of the oceanic crust. We found crustal thicknesses of 5.6–5.9 km under the transform fault to produce the best fit of the PmP phase arrivals and Pg/Pn crossovers. Since the crust is not thin beneath the transform parallel troughs and the velocity anomaly is not confined to the median ridge, we find uplift by serpentinite diapirs unlikely as an explanation for the relief of the median ridge. A median ridge that is the result of brittle deformation due to compression across the transform domain is, however, compatible with our results. The upper crust is thicker to the north of the transform than to the south, which is likely a consequence of the contrast in temperature structure of these two spreading segments.