A vertex z in a connected graph G resolves two vertices u and v in G if d G (u, z) ̸ = d G (v, z). A set of vertices R G {u, v} is a set of all resolving vertices of u and v in G. For every two distinct vertices u and v in G, a resolving function f of G is a real function f : V (G) → [0, 1] such that f (R G {u, v}) ≥ 1. The minimum value of f (V (G)) from all resolving functions f of G is called the fractional metric dimension of G. In this paper, we consider a graph which is obtained by the comb product between two connected graphs G and H, denoted by G £o H. For any connected graphs G, we determine the fractional metric dimension of G £o H where H is a connected graph having a stem or a major vertex.