The dynamic process of charge injection is investigated for an open conjugated polymer chain in contact with a metal electrode in the framework of a nonadiabatic approach. It is found that the injected charges form wave packets due to the strong electron-lattice interactions in the conjugated polymer. A wave packet may contain any quantity of charges up to two electronic units, which depends upon the injection condition. As the system is spin degenerate within the present model, a wave packet has no spin. Discrete energy levels will appear in the gap accompanying the wave packet, which results in potential asymmetry of the charge injection and ejection between the metal electrode and the polymer. The asymmetry can be used to explain the electrical hysteresis in organic devices. It is found that there exists an upper critical field or forming field, beyond which the injected charges could not form a wave packet. Under a strong driving electric field, it is also found that a wave packet will dissociate into an extended state. The dependence of the dissociating field on the charge quantity a wave packet contains is studied.