This book constitutes the refereed proceedings of the Thailand-Japan Joint Conference on Computational Geometry and Graphs, TJJCCGG 2012, held in Bangkok, Thailand, in December 2012. The 15 original research papers presented were selected from among six plenary talks, one special public talk and 41 talks by participants from about 20 countries around the world. TJJCCGG 2012 provided a forum for researchers working in computational geometry, graph theory/algorithms and their applications.