Let be an integer and G a simple graph with vertex set V(G). Let f be a function that assigns labels from the set to the vertices of G. For a vertex the active neighbourhood AN(v) of v is the set of all vertices w adjacent to v such that A [k]-Roman dominating function (or [k]-RDF for short) is a function satisfying the condition that for any vertex with f(v) < k, The weight of a [k]-RDF is and the [k]-Roman domination number of G is the minimum weight of an [k]-RDF on G. In this paper we shall be interested in the study of the [k]-Roman domination subdivision number sd of G defined as the minimum number of edges that must be subdivided, each once, in order to increase the [k]-Roman domination number. We first show that the decision problem associated with sd is NP-hard. Then various properties and bounds are established.