Graphene aerogels (GAs) are a kind of advanced graphene assemblies, which are quite elastic and can easily restore their original form after compression. The macroscale compression behavior of the GAs is the result of microstructural evolution of the graphene sheets. In this paper, the microstructural compression response of honeycomb-like GAs is investigated via coarse-grained molecular dynamics (CGMD) method. Based on the coarse-grained (CG) model of a single-layer graphene, honeycomb-like structures can be built and arranged layer-by-layer to form the complete GA model. CGMD simulations presented in this work are carried out with a TersoffCG potential, which was developed specifically for single-layer graphene. The effects of layer number, size of the graphene sheets and the interlaminar overlap pattern on the compressive behavior of the GAs are studied. Moreover, the stress distribution in graphene networks of the GAs during the compression process is analyzed. Different microscale strain concentrations and stress localizations are discovered in the GAs with different network patterns. Furthermore, a negative Poisson's ratio of the models within a certain range of compressive strain is found, which is related to both the microstructural arrangement and the deformation of graphene sheet. (C) 2018 Elsevier Ltd. All rights reserved.