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 $sim 1times10^{32}$ 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 primarys 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.
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