From the perspective of large system, a directed complex dynamic network (DCDN) is regarded as being made up of the nodes subsystem (NS) and the links subsystem (LS), which are coupled to each other. Different from previous studies, which propose the dynamic model of LS with the matrix differential equations, this paper describes the dynamic behaviour of LS with the outgoing links vector at every node, by which the dynamic model of LS can be represented as the vector differential equation to form the outgoing links subsystem (OLS). Due to the fact that vectors have more flexible mathematical properties than matrices, this paper proposes the more convenient mathematic method to investigate the double tracking control problem of NS and OLS. Under the condition that the states of NS are available and the states of OLS are unavailable, the asymptotical state observer of OLS is designed, by which the tracking controllers of NS and OLS are synthesised to ensure achieving the double tracking goals. Finally, an example simulation for supporting the theoretical results is also provided.