  Photometric observations for the totally eclipsing binary system TYC
4002-2628-1, were obtained between November 2020 and November 2021. To
determine the stellar atmospheric parameters, a spectral image was taken with
the 2.16 m telescope at National Astronomical Observatory of China (NAOC). TYC
4002-2628-1 is a low-amplitude (about 0.15 mag for $V$ band), short-period
(0.3670495 d), contact eclipsing binary with a total secondary eclipse.
Intrinsic light curve variations and the reversal of the O'Connell effect are
detected in the light curves, which may be due to spot activity. Based on the
photometric solutions derived from the multi-band time series light curves, TYC
4002-2628-1 is an extremely low mass ratio contact binary with a mass ratio of
$q\sim$ 0.0482 and a fill-out factor of $f\sim5\%$. By analyzing the $O-C$
variations, we find that its orbital period remains unchanged when BJD <
2458321 . Then the orbital period changed suddenly around BJD 2458743 and has
an increasing rate of $dP/dt=1.62\times{10^{-5}}day\cdot yr^{-1}=140$
$second\cdot century^{-1}$ .
  If confirmed, TYC 4002-2628-1 would be the contact binary with the highest
orbital period increasing rate so far. By investigating the ratio of orbital
angular momentum to the spin angular momentum ( $J_{orb}$/$J_{spin}$ $<3$) ,
the instability mass ratio ($q_{inst}/q=1.84$) and the instability separation
($A_{inst}/A=1.35$), TYC 4002-2628-1 can be regarded as a merger candidate.
