Our goal was to improve the fundamental parameters of the massive close double-lined eclipsing B2.5V+B2.5V binary CV Velorum. We gathered new high-resolution echelle spectroscopy on 13 almost consecutive nights covering two orbits. We computed a simultaneous solution to all the available high-quality radial-velocity and light data with the latest version of the Wilson-Deviney code. We obtained the following values for the physical parameters: M1=6.066(74)M☉, M2=5.972(70)M☉, R1=4.126(24)R☉, R2=3.908(27)R☉, logL1=3.20(5)L☉, and logL2=3.14(5)L☉. The quoted errors contain a realistic estimate of systematic uncertainties mainly stemming from the effective temperature estimation. We derived abundances for both components and found them to be compatible with those of B stars in the solar neighbourhood. We discovered low-amplitude periodic line-profile variations with the orbital frequency for both components. Their interpretation requires new data with a longer time span. The primary rotates subsynchronously while the secondary's vsin i and radius are compatible with synchronous rotation. We provide an update of the empirical mass-luminosity relation for main-sequence B stars which can be used for statistical predictions of masses or luminosities.