We present a study of the evolution of the galaxy Velocity Dispersion Function ( VDF ) from z = 0 to z = 1.5 using photometric data from the UDS and NMBS COSMOS surveys . The VDF has been measured locally using direct kinematic measurements from the Sloan Digital Sky Survey , but direct studies of the VDF at high redshift are difficult as they require velocity dispersion measurements of many thousands of galaxies . Taylor et al . ( 2010 ) demonstrated that dynamical and stellar mass are linearly related when the structure of the galaxy is accounted for . We show that the stellar mass , size and Sérsic index can reliably predict the velocity dispersions of SDSS galaxies . We apply this relation to galaxies at high redshift and determine the evolution of the inferred VDF . We find that the VDF at z \sim 0.5 is very similar to the VDF at z = 0 . At higher redshifts , we find that the number density of galaxies with dispersions \lesssim 200 \mathrm { km / s } is lower , but the number of high dispersion galaxies is constant or even higher . At fixed cumulative number density , the velocity dispersions of galaxies with \log N [ \mathrm { Mpc ^ { -3 } } ] < -3.5 increase with time by a factor of \sim 1.4 from z \sim 1.5 - 0 , whereas the dispersions of galaxies with lower number density are approximately constant or decrease with time . The VDF appears to show less evolution than the stellar mass function , particularly at the lowest number densities . We note that these results are still somewhat uncertain and we suggest several avenues for further calibrating the inferred velocity dispersions .