This technical note studies the well-known Vicsek model with bounded time-varying delays. We consider the case that the communication delays appear in both position and heading transmissions, which is more realistic in practice. We derive delay-dependent conditions, imposed only on the initial state, to guarantee synchronization of the delayed linear and nonlinear Vicsek models. It is further seen from our simulations that the Vicsek model is indeed sensitive to communication delays in the sense that a large delay can destroy the synchronization behavior.