Many graph-theoretic concepts have both vertex and edge versions. Examples are cut-vertex , cut-edge , vertex-integrity ( integrity ), edge-integrity , vertex coloring , edge coloring , and vertex-connectivity , edge-connectivity . Frank Harary et al. defined the geodetic number of a graph for vertices in [Chartrand, G., Harary, F. and Zhang, P. (2002). On the geodetic number of a graph. Networks , 39 , 1-6; Chartrand, G., Harary, F. and Zhang, P. (2000). Geodetic sets in graphs. Discussions Mathematicae Graph Theory , 20 , 129-138; Harary, F., Loukakis, E. and Tsours, C. (1993). The geodetic number of a graph. Mathl. Comput. Modelling , 17 (11), 89-93]. In this study we give a definition of the edge geodetic number for a graph and derive some results.