We employ a bias-corrected abundance-matching technique to investigate the coevolution of the Lambda cold dark matter (ΛCDM) dark halo mass function (HMF), the observationally derived velocity dispersion and stellar mass functions (VDF, SMF) of galaxies between z= 1 and 0. We use for the first time the evolution of the VDF constrained through strong lensing statistics by Chae for galaxy–halo abundance-matching studies. As a local benchmark we use a couple of z∼ 0 VDFs [a Monte Carlo realized VDF based on Sloan Digital Sky Survey (SDSS) Data Release 5 (DR5) and a directly measured VDF based on SDSS DR6]. We then focus on connecting the VDF evolution to the HMF evolution predicted by N-body simulations and the SMF evolution constrained by galaxy surveys. On the VDF–HMF connection, we find that the local dark halo virial mass–central stellar velocity dispersion (Mvir–σ) relation is in good agreement with the individual properties of well-studied low-redshift dark haloes, and the VDF evolution closely parallels the HMF evolution meaning little evolution in the Mvir–σ relation. On the VDF–SMF connection, it is also likely that the stellar mass–stellar velocity dispersion (M★–σ) relation evolves little, taking the abundance-matching results together with other independent observational results and hydrodynamic simulation results. Our results support the simple picture that as the halo grows hierarchically, the stellar mass and the central stellar velocity dispersion grow in parallel. We discuss possible implications of this parallel coevolution for galaxy formation and evolution under the ΛCDM paradigm.