There exists a special class of X-ray pulsars that exhibit very slow pulsation of Pspin > 1000 s in the high mass X-ray binaries (HMXBs). We have studied the temporal and spectral properties of these superslow pulsation neutron star binaries in hard X-ray bands with INTEGRAL observations. Long-term monitoring observations find spin period evolution of two sources: spin-down trend for 4U 2206+54 (Pspin ~ 5560 s with Ṗspin ~ 4.9 × 10−7 s s−1) and long-term spin-up trend for 2S 0114+65 (Pspin ~ 9600 s with Ṗspin ~ −1 × 10−6 s s−1) in the last 20 years. A Be X-ray transient, SXP 1062 (Pspin ~ 1062 s), also showed a fast spin-down rate of Ṗspin ~ 3 × 10−6 s s−1 during an outburst. These superslow pulsation neutron stars cannot be produced in the standard X-ray binary evolution model unless the neutron star has a much stronger surface magnetic field (B > 1014 G). The physical origin of the superslow spin period is still unclear. The possible origin and evolution channels of the superslow pulsation X-ray pulsars are discussed. Superslow pulsation X-ray pulsars could be younger X-ray binary systems, still in the fast evolution phase preceding the final equilibrium state. Alternatively, they could be a new class of neutron star system – accreting magnetars.