  The measurements of quasi-periodic oscillations (QPOs) provide a quite
powerful tool to test the nature of astrophysical black hole candidates in the
strong gravitational field regime. In this paper, we use QPOs within the
relativistic precession model to test a recently proposed family of rotating
black hole mimickers, which reduce to the Kerr metric in a limiting case, and
can represent traversable wormholes or regular black holes with one or two
horizons, depending on the values of the parameters. In particular, assuming
that the compact object of GRO J1655-40 is described by a rotating black hole
mimicker, we perform a $\chi$-square analysis to fit the parameters of the
mimicker with two sets of observed QPO frequencies from GRO J1655-40. Our
results indicate that although the metric around the compact object of GRO
J1655-40 is consistent with the Kerr metric, a regular black hole with one
horizon is favored by the observation data of GRO J1655-40.
