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We report the timing and broad-band spectral properties of the Be transient high-mass X-ray binary pulsar GRO J1008-57 using a Suzaku observation in the declining phase of its 2007 November and December outbursts. Pulsations with a period of 93.737 s were clearly detected in the light curves of the pulsar up to the 80-100 keV energy band. The pulse profile was found to be strongly energy dependent, a double-peaked profile at soft X-ray energy bands (<8 keV) and a single-peaked smooth profile at hard X-rays. The broad-band energy spectrum of the pulsar, reported for the first instance in this paper, is well described with three different continuum models, namely (i) a high energy cut-off power law, (ii) a Negative and Positive power law with EXponential (NPEX) cut-off and (iii) a partial covering power law with high energy cut-off. In spite of large value of absorption column density in the direction of the pulsar, a blackbody component of temperature ∼0.17 keV for the soft excess was required for the first two continuum models. A narrow iron Kα emission line was detected in the pulsar spectrum. The partial covering model, however, is found to explain the phase-averaged and phase-resolved spectra well. The dip-like feature in the pulse profile can be explained by the presence of an additional absorption component with high column density and covering fraction at the same pulse phase. The details of the results are described in the paper.