Abstract: Droplet impacts on meshes are ubiquitous both in nature and in a variety of applications. The impact may lead to liquid penetration through the mesh and formation of secondary droplets underneath the mesh, or spreading on the mesh and no occurrence of penetration. In either situation, liquid remains on the meshes and forms pre-wetted meshes after impacts, leading to different following impact outcomes compared with impacts on dry meshes. However, previous studies focused on impacts of low-viscosity droplets on dry meshes. The evolution and mechanism of viscous Newtonian droplets impacts on dry or pre-wetted meshes remain to be explored. In this paper, the liquid fingers and the fragmentation occurred underneath the mesh following a viscous droplet (aqueous glycerol solution) impacting a dry or pre-wetted mesh are investigated using high-speed shadow imaging technology, with special attention paid on the influence of mesh size, droplet viscosity and pre-wetted liquid film thickness on impact outcomes. It was observed that both a decrease of mesh size and an increase of droplet viscosity resulted in a decrease of maximum length of liquid finger and suppressed a complete penetration through a dry mesh, an increase of pre-wetted liquid film thickness suppressed a complete penetration and resulted in a decrease of maximum length of liquid finger. Considering the influence of mesh size, droplet viscosity, and pre-wetted liquid film thickness, theoretical models for predicting the maximum length of liquid finger when incomplete penetration occurs and for predicting the threshold parameters for complete penetration is proposed and is validated by comparisons with experimental results.