Let $G = (V, E)$ be a simple graph. A set $S \subseteq V$ is a fair dominating set of $G$, if every vertex not in $S$ is adjacent to one or more vertices in $S$. A dominating set $S$ of $G$ is a fair dominating set if every two vertices $u, v \in V(G) \setminus S$ are dominated by same number of vertices from $S$. The minimum cardinality taken over all fair dominating sets in $G$ is called the fair domination number of $G$ and is denoted by $\gamma_f(G)$. Let $W_{1,n}$ be wheel graph of order $n + 1$. Let $W_{1,n}^i$ be the family of all fair dominating sets of a wheel $W_{1,n}$ with cardinality $i$, and let $d_f(W_{1,n}, i) = |W_{1,n}^i|$. In this paper, we explore the fair domination polynomial of a wheel graph and also more properties are obtained in it.