Results of ideal-magnetohydrodynamic (MHD) numerical simulations of relativistic jets are presented. It is found that initially Poynting flux-dominated jets can be effectively accelerated to high bulk Lorentz factors with an efficiency (defined as the ratio of the final kinetic energy flux to the total energy flux) of the order of 50%. The connection between the collimation of the flow, which is manifested in the curved streamlines, and the acceleration process is analyzed. In validating the basic features of previous semi-analytic (radially self-similar) solutions for steady-state flows, these numerical results go a long way toward establishing an "MHD acceleration and collimation paradigm" for relativistic astrophysical jets.