We investigate a unique accreting millisecond pulsar with X-ray eclipses, SWIFT J1749.4-2807 （hereafter J1749）, and try to set limits on the binary system by various methods including use of the Roche lobe, the mass-radius relations of both main sequence （MS） and 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 is 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 an MS one. For the case that the radius equals its Roche one, we have a companion star with mass M ≈ 0.51 Me and radius Rc ≈ 0.52 R⊙, and the inclination angle is i ≈ 76.5°; for the case that the radius reaches 90% of its Roche one, we have M ≈ 0.43M⊙, Rc ≈ 0.44R⊙ and i ≈ 75.7°. We also obtain the mass of J1749, Mp ≈ 1 M⊙, 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 - 0.3. The relatively low pulsar mass （about - M⊙） 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.
