$SLEE$ has various applications in a large variety of problems. The signless Laplacian Estrada index of a hypergraph H is defined as $SLEE\left(H\right)={\sum }_{i=1}^n{e}^{{\lambda }_i\left(Q\right)}$, where ${\lambda }_1\left(Q\right),{\lambda }_2\left(Q\right),\dots ,{\lambda }_n\left(Q\right)$ are the eigenvalues of the signless Laplacian matrix of H. In this paper, we characterize the unique r-uniform unicyclic hypergraphs with maximum and minimum $SLEE$.