Let $G$ be a simple graph. A dominating set $D$ is a strong split dominating set if the induced subgraph $\langle V(D) \rangle$ is totally disconnected with at least two vertices. Let $\mathcal{D}_{ss}^k(G)$ be the family of strong split dominating sets of $G$ of cardinality $k$ and $d_{ss}(G,k) = |\mathcal{D}_{ss}^k(G)|$. We define the strong split domination polynomial of a graph $G$ of order $n$ as the polynomial $D_{ss}(G,x) = \sum_{k=\gamma_{ss}(G)}^{\lfloor n/2 \rfloor} d_{ss}(G,k) x^k$. In this paper, we determine the strong split domination polynomial of paths and obtain some of its properties.