  We investigate an unique accreting millisecond pulsar with X-ray eclipses,
SWIFT J1749.4$-$2807 (hereafter J1749), and try to limit the binary system by
various methods including that of the Roche lobe, the mass-radius relations of
both a main sequence (MS) and a white dwarf (WD) companion stars, as well as
the measured mass function of the pulsar. The calculations are based on the
assumption that the radius of the companion star has reached its Roche radius
(or at 90%), but the pulsar's mass has not been assumed to be a certain value.
Our results are as follows. The companion star should be a MS. For the case
that the radius equals to its Roche one, we have a companion star with mass
$M\simeq 0.51 M_{\odot}$ and radius $R_{\rm c}\simeq 0.52R_{\odot}$, and the
inclination angle is $i\simeq 76.5^{\circ}$; for the case that the radius
reaches 90% of its Roche one, we have $M\simeq 0.43M_{\odot}$, $R_{\rm c}\simeq
0.44R_{\odot}$ and $i\simeq 75.7^{\circ}$. We also obtain the mass of J1749,
$M_{\rm p}\simeq 1M_\odot$, and conclude that the pulsar could be a quark star
if the ratio of the critical frequency of rotation-mode instability to the
Keplerian one is higher than $\sim 0.3$. The relatively low pulsar mass (about
$\sim M_\odot$) may also challenge the conventional recycling scenario for the
origin and evolution of millisecond pulsars. The results presented in this
paper are expected to be tested by future observations.
