A distorted Frank-Kasper polyhedral structure (A) as the putative global minimum was identified for the neutral and charged V-17 clusters by using the Monte Carlo basin-hopping algorithm based on semi-empirical Gupta potential and density functional theory calculations. The cationic V-17(+) cluster reproduces well the experimental infrared multiple photon dissociation spectroscopy, and the calculated adiabatic ionization potentials and electron affinities of the A structure are close to its experimental values. It is also found that the shell-closed V-17(+) structure can be stabilized by 20 delocalized 3e-2e and 4 delocalized 6e-2e sigma bonds on the outer shell and 12 delocalized 4e-2e sigma bonds on the inner shell. Our results will inevitably stimulate future theoretical and experimental studies for the design and exploration of largely nanoscale materials.