An oriented graph Gσ is a digraph without loops and multiple arcs, where G is called the underlying graph of Gσ. Let S(Gσ) denote the skew-adjacency matrix of Gσ, and A(G) be the adjacency matrix of G. The skew-rank of Gσ, written as sr(Gσ), refers to the rank of S(Gσ), which is always even since S(Gσ) is skew symmetric.A natural problem is: How about the relation between the skew-rank of an oriented graphGσand the rank of its underlying graph? In this paper, we focus our attention on this problem. Denote by d(G) the dimension of cycle spaces of G, that is d(G)=|E(G)|−|V(G)|+θ(G), where θ(G) denotes the number of connected components of G. It is proved that sr(Gσ)≤r(G)+2d(G) for an oriented graph Gσ, the oriented graphs Gσ whose skew-rank attains the upper bound are characterized.