Dynamic multi-layer network analysis is the frontier direction of network science and a prominent challenge in the field of complex network systems. In this paper, a covariate-assisted dynamic multi-layer network community detection method is proposed, which effectively combines the dependence within each network, across time and between different layers. The latent Gaussian process is used to model the edge probability between participants, and a flexible time series analysis is obtained. An extended model based on community is proposed to reduce the computational burden. In terms of parameter estimation, this paper uses the Bayesian method to conduct posterior inference on model parameters. Finally, a set of real business relationship network data is used for experiments, and the results show that the dynamic multilayer block network model has lower estimation time cost and better prediction performance, and the chunking structure of its model is more capable of revealing meaningful community structures, which makes it suitable for dealing with more complex dynamic networks.