The {\em eccentricity} of a vertex $v$ is the maximum distance between $v$ and any other vertex‎. ‎A vertex with maximum eccentricity is called a peripheral vertex‎. ‎The peripheral Wiener index $PW(G)$ of a graph $G$ is‎ ‎defined as the sum of the distances between all pairs of peripheral vertices of $G$‎. ‎In this paper‎, ‎we initiate the study of the peripheral Wiener index and investigate‎ ‎its basic properties‎. ‎In particular‎, ‎we determine the peripheral‎ ‎Wiener index of the cartesian product of two graphs and trees‎.