Abstract: Complex network is a hot spot in network science research. With the deepening of research, the research focus of complex network is shifting from single-layer network to multi-layer directed network closer to actual network. Based on the master stability function method, the eigenvalue spectrum and synchronization ability of the four-layer unidirectional coupled star network are studied. The eigenvalue spectrum of the supra-Laplace matrix of the four-layer unidirectional coupled star network is given. The relationship between the synchronization ability of the K layer unidirectional coupled star network and the node number, the number of layers, the intra-layer coupling strength and the inter-layer coupling strength are analyzed under the condition that the synchronization domain is bounded and unbounded. Finally, the simulation image of synchronization ability of K layer-by-layer unidirectional coupled star network is given（K=15）.