A 2-rainbow domination function of a graph G is a function fthat assigns to each vertex a set of colors chosen from the set {1, 2} i.e. ( ) ({ }), such that for any ( ) ( ) ; implies⋃ ( ) { } ( )The 2-rainbow domination number ( ) of a graph G is the minimum ( ) Σ| ( )| ( )over all such functions f.The Hexagonal networks are popular mesh-derived parallel architectures. In this paper we present an upper bound for the 2-rainbow domination number of hexagonal networks.