  We investigate the invariant-mass distribution of top-quark pairs near the
$2m_t$ threshold, which has strong impact on the determination of the top-quark
mass $m_t$. We show that higher-order non-relativistic corrections lead to
large contributions which are not included in the state-of-the-art theoretical
predictions. We derive a factorization formula to resum such corrections to all
orders in the strong-coupling, and calculate necessary ingredients to perform
the resummation at next-to-leading power. We combine the resummation with
fixed-order results and present phenomenologically relevant numeric results. We
find that the resummation effect significantly enhances the differential cross
section in the threshold region, and makes the theoretical prediction more
compatible with experimental data. We estimate that using our prediction in the
determination of $m_t$ will lead to a value closer to the result of direct
measurement.
