Abstract A set S VG ⊆ ( ) is called a geodetic set if every vertex of G lies on a shortest u-v path for some uv S , ∈ , the minimum cardinality among all geodetic sets is called geodetic number and is denoted by g G n ( ). A set C VG ⊆ ( ) is called a chromatic set if C contains all vertices of different colors in G, the minimum cardinality among all chromatic sets is called the chromatic number and is denoted by χ (G) . A geo-chromatic set S VG c ⊆ ( ) is both a geodetic set and a chromatic set. The geo-chromatic number χ gc (G) of G is the minimum cardinality among all geo-chromatic sets of G. In this paper, we determine the geodetic number and the geo-chromatic number of 2-cartesian product of some standard graphs like complete graphs, cycles and paths.