  PSR J1537+1155, also known as PSR B1534+12, is the second discovered double
neutron star (DNS) binary. More than 20 years of timing observations of PSR
J1537+1155 have offered some of the most precise tests of general relativity
(GR) in the strong-field regime. As one of these tests, the gravitational-wave
emission predicted by GR has been probed with the significant orbital decay
($\dot{P}_\mathrm{b}$) of PSR J1537+1155. However, compared to most GR tests
provided with the post-Keplerian parameters, the orbital-decay test was lagging
behind in terms of both precision and consistency with GR, limited by the
uncertain distance of PSR J1537+1155. With an astrometric campaign spanning 6
years using the Very Long Baseline Array, we measured an annual geometric
parallax of $1.063\pm0.075$ mas for PSR J1537+1155, corresponding to a distance
of $0.94^{+0.07}_{-0.06}$ kpc. This is the most tightly-constrained
model-independent distance achieved for a DNS to date. After obtaining
$\dot{P}_\mathrm{b}^\mathrm{Gal}$ (i.e., the orbital decay caused by Galactic
gravitational potential) with a combination of 4 Galactic mass distribution
models, we updated the ratio of the observed intrinsic orbital decay to the GR
prediction to $0.977\pm0.020$, three times more precise than the previous
orbital-decay test ($0.91\pm0.06$) made with PSR J1537+1155.
