  IGR J00370+6122 is a high-mass X-ray binary, of which the primary is a B1 Ib
star, whereas the companion is suggested to be a neutron star by the detection
of 346-s pulsation in one-off 4-ks observation. To better understand the nature
of the compact companion, the present work performs timing and spectral studies
of the X-ray data of this object, taken with XMM-Newton, Swift, Suzaku, RXTE,
and INTEGRAL. In the XMM-Newton data, a sign of coherent 674 s pulsation was
detected, for which the previous 346-s period may be the 2nd harmonic. The
spectra exhibited the "harder when brighter" trend in the 1$-$10 keV range, and
a flat continuum without clear cutoff in the 10$-$80 keV range. These
properties are both similar to those observed from several low-luminosity
accreting pulsars, including X Persei in particular. Thus, the compact object
in IGR J00370+6122 is considered to be a magnetized neutron star with a rather
low luminosity. The orbital period was refined to $15.6649 \pm 0.0014$ d. Along
the orbit, the luminosity changes by 3 orders of magnitude, involving a sudden
drop from $\sim 4 \times 10^{33}$ to $\sim 1\times10^{32}$ erg s$^{-1}$ at an
orbital phase of 0.3 (and probably vice verse at 0.95). Although these
phenomena cannot be explained by a simple Hoyle-Lyttleton accretion from the
primary's stellar winds, they can be explained when incorporating the propeller
effect with a strong dipole magnetic field of $\sim 5 \times10^{13}$ G.
Therefore, the neutron star in IGR J00370+6122 may have a stronger magnetic
field compared to ordinary X-ray pulsars.
