In this paper, aiming at the problem of different signals acting on the same node on a complex network with double time delay, two independent chaotic systems are established, a complex network model with both node delay and coupling delay is constructed. And the synchronization error condition of complex networks with double time delay is analyzed, by applying appropriate pinning controller on the complex network nodes with double time delay, some network nodes are controlled to investigate the problem of hybrid synchronization. Selecting the appropriate Lyapunov function, basing on the Lasalle invariance principle and the linear matrix inequality characteristic, the sufficient conditions for hybrid synchronization of node delay and coupling delay complex networks are given. Finally, the numerical simulation is presented, and the results indicate it is feasible and verified to realize the hybrid synchronization of two independent chaotic systems on the complex network with node delay and coupling delay.