Over the past decades, the synchronization of complex networks with directed topologies has received considerable attention owing to its extensive applications in the realistic world. Design of proportional-integral-derivative (PID) control protocols for achieving synchronization with directed networks is known to be a challenging task. The purpose of this paper is to establish a connection between the PID control protocols and synchronization of complex dynamical networks with directed topologies. Based on the classical complex network model, we investigate global synchronization with PD controller of a balanced strongly connected directed network and global synchronization with PI controller of a strongly connected directed network, and a directed network containing a spanning tree, respectively. Several sets of sufficient conditions are established under which the network reaches global synchronization. The simulation examples are presented to verify the efficiency of the theoretical results.