Let G be a connected graph and d(x,y) be the distance between the vertices x and y. A subset of vertices W = { w₁, ..., w_k } is called a resolving set for G if for every two distinct vertices x, y ∈ V(G) there is a vertex w_i ∈ W such that d(x,w_i) ≠ d(y,w_i). A resolving set containing a minimum number of vertices is called a metric basis for G and the number of vertices in a metric basis is its metric dimension dim(G). Let J_2n be the graph obtained from the wheel W_2n by alternately deleting n spokes. In this note it is shown that dim(J_2n)= ⌊ 2n/3 ⌋ for every n ≥ 4.