We propose an enhanced multiple-pass group delay (GD) measurement scheme of fiber-Bragg grating (FBG) based on optical low-coherence reflectometry (OLCR). The fiber loop embedded with the measured FBG is innovatively applied to the OLCR-based system, and the probe signal light can go through the FBG repeatedly. In the multiple-pass propagation of light, the FBG-induced GD or chromatic dispersion is amplified. After the straightforward reduction, the GD of FBG can be recovered accurately. And the triple-pass measurements are demonstrated in detail. Compared to the conventional single-pass scheme, the repeatability of GD in our measurements (<0.4ps) is improved more than 2 times. The multiple-pass scheme can be expected to break the limit of the GD resolution in the existing FBG measurement methods. In addition, using the polarization controllers (PC) in the fiber loop, the weak polarization differential group delay (DGD) or polarization mode dispersion (PMD) of FBG is measured and discussed. It should be interesting to the characterization of the ultraviolet (UV) or mechanical induced birefringence in photosensitive optical fibers. The multiple-pass measurement scheme of FBG could also be expected to realize two-parameter sensing.