The　complexity　of　polyhedral　block　systems　(e.g.,　small　blocks,　flat　blocks　with　small　angles,　edges,　or　faces)　poses　challenges　in　the　kinetic　analysis　of　rock　block　systems.　This　paper　proposed　an　improved　potential-based　penalty　function　approach　within　an　explicit　three-dimensional　(3D)　discontinuous　deformation　analysis　(DDA)　framework　for　efficient　and　robust　kinetic　analysis　of　rock　block　systems.　An　explicit　formulation　of　3D　DDA　based　on　velocity　verlet　algorithm　is　first　derived.　A　novel　definition　of　potential　function　is　then　proposed　with　details　of　the　key　algorithms　for　overlap　judgment　of　convex　polyhedron,　construction　of　intersection　polyhedron　and　numerical　integral　for　computation　of　contact　force.　The　improved　potential-based　penalty　function　method　is　robust　and　efficient　for　complex　convex　polyhedral　shapes.　Several　benchmark　and　application　examples　verify　the　feasibility,　accuracy　and　robustness　of　the　proposed　methods　in　solving　contact　of　polyhedral　block　systems.　(C)　2020　Elsevier　Inc.　All　rights　reserved.