We investigate the elastic properties and phonon dispersion of the body-centered cubic structure vanadium $(V)$ under pressure by using the generalized gradient approximation (GGA). Our elastic constants of $V$ at zero pressure and zero temperature are in good agreement with the available experimental data and other theoretical data. The pressure dependences of bulk modulus $B$ and its pressure derivative $B',$ shear modulus $G,$ elastic Debye temperature $\Theta_E,$ elastic anisotropy factor $A,$ Poisson ratios $σ$ and Kleinmann parameter $ζ$ are also presented. An analysis for the calculated elastic constants has been made to reveal the mechanical unstability of $V$ up to 100 GPa. For the phonon dispersions of $V,$ it is easily seen that the phonon frequencies increase as the volume decreases, the phonon mode linked to a Kohn anomaly has softened to negative values.