  Spin period variations and hard X-ray spectral properties of Be/X-ray pulsar
GRO J1008-57 are studied with INTEGRAL observations. The pulsation periods at
93.66 s in 2004 and at 93.73 s in 2009 are determined. Pulse profiles of GRO
J1008-57 during outbursts are energy dependent: double-peak profile in soft
bands of 3-7 keV and single-peak profile in hard X-rays above 7 keV. GRO
J1008-57 has undergone a spin-down trend from 1993-2009 with a rate of
4.1x10^-5 s day^-1, and might transfer into a spin-up trend after 2009. The
spectra from 3-100 keV of GRO J1008-57 during outbursts are fitted with photon
index of 1.4 and cutoff energies of 23-29 keV. We find a relatively soft
spectrum in early phase of the 2009 outburst with cutoff energy 13 keV. Above a
hard X-ray flux of 10^-9 erg cm^-2 s^-1, the spectra of GRO J1008-57 during
outbursts need an enhanced hydrogen absorption of column density 6x10^22 cm^-2.
The observed dip-like pulse profile of GRO J1008-57 in soft X-ray bands should
be caused by this intrinsic absorption. Around the outburst peaks, a possible
cyclotron resonance scattering feature at 74 keV is detected in the spectra of
GRO J1008-57, making the source as the neutron star of highest magnetic field
(6.6x10^12 G) in known accreting X-ray pulsars. Two modulations periods at
124.38 and 248.78 days are found using RXTE/ASM light curves of GRO J1008-57.
Two flare peaks appearing in the folded light curve have different spectral
properties. The normal outburst lasting 0.1 orbital phase has a hard spectrum
and cannot be detected below 3 keV. The second flare lasting ten days shows a
very soft spectrum without significant detections above 5 keV. Lack of soft
X-ray emissions in outbursts should be caused by the enhanced hydrogen
absorption near the periastron passage. Soft spectral origins in the second
flares still need further detailed studies with soft X-ray spectroscopies.
