The multi-layer directed network model focuses on portraying the directionality, diversity and difference of the edges in the network. It is also one of the powerful tools for analyzing the complexity of the network system and the heterogeneous interaction characteristics between network layers. This paper constructs three three-layer directed network models combined with traditional complex network theory and analyzes their degree distribution characteristics. By controlling the out-degree and in-degree of the middle-level nodes, a network structure with multi-peak characteristics is configured. Combined with numerical simulation, it is concluded that the number of links between the layers of the directed network makes the network characterize the characteristics of unimodal, bimodal, and trimodal; the combination of the optimal mechanism and the changes in the number of inter-layer links, the network characteristics show the coexistence of power law and unimodal. The research results of this paper have practical value for the analysis of network generation mechanism and correlation law by using multi-layer directed network theory in the era of big data.