<p>Given a finite group $ G $ with the identity $ e $, the TI-power graph (trivial intersection power graph) of $ G $ is an undirected graph with vertex set $ G $, in which two distinct vertices $ x $ and $ y $ are adjacent if $ \langle x\rangle\cap \langle y\rangle = \{e\} $. In this paper, we obtain closed formulas for the metric and strong metric dimensions of the TI-power graph of a finite group. As applications, we compute the metric and strong metric dimensions of the TI-power graph of a cyclic group, a dihedral group, a generalized quaternion group, and a semi-dihedral group.</p>