We performed a detailed study of the timing performance of the LHCb VELO Timepix3 Telescope with a 180 GeV/c mixed hadron beam at the CERN SPS. A twofold method was developed to improve the resolution of single-plane time measurements, resulting in a more precise overall track time measurement. The first step uses spatial information of reconstructed tracks in combination with the measured signal charge in the sensor to correct for a mixture of different effects: variations in charge carrier drift time; variations in signal induction, which are the result of a non-uniform weighting field in the pixels; and lastly, timewalk in the analog front-end. The second step corrects for systematic timing offsets in Timepix3 that vary from -2 ns to 2 ns. By applying this method, we improved the track time resolution from 438$,pm,$16 ps to 276$,pm,$4 ps.
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