A java-based graphical tool for drawing Feynman diagrams is presented. It differs from similar existing tools in various respects. For example, it is based on models, consisting of particles (lines) and (optionally) vertices, each of which can be given their individual properties (line style, color, arrows, label, etc.). The diagrams can be exported in any standard image format, or as PDF. Aside from its plain graphical aspect, the goal of FeynGame is also educative, as it can check a Feynman diagrams validity. This provides the basis to play games with diagrams, for example. Here we describe one such game where a given set of initial and final states must be connected through a Feynman diagram within a given interaction model.