This paper studies the synchronization problem of complex-valued multi-layer networks (CVMLNs) via delay-dependent pinning impulsive control. At first, a multi-layer directed network model is constructed in complex domains, and the effects of intra-layer and inter-layer coupling delays are both considered. In order to achieve synchronization of CVMLNs, a delay-dependent pinning impulsive control strategy is designed in the complex field. The pinning impulsive controller depends on not only the network states at each impulsive instant but also the states at history time. By taking advantage of the Lyapunov function method in the complex field and algebraic graph theory, sufficient conditions for synchronization of CVMLNs with time-varying coupling delays are established. Finally, a numerical example is presented to illustrate the effectiveness and validity of the theoretical result.