The shock metamorphism of 47 H group chondrites (H-chondrites) from the Grove Mountains including undulatory extinction, planar fractures, mosaic extinction, shock veins and pockets, and dendritic eutectic metal-sulfide, is observed through optical microscope. The textures and assemblages of shock veins in these H-chondrites are examined by the scanning electron microscope. Based on observations of the above shock effects, the shock stages of the 47 H-chondrites are classified into S1(5), S2(19), S3(14), S4(8) and S5(1). Of these H-chondrites, GRV 022469 has the highest(S5) shock stage. The comparison of shock stages in these H-chondrites with L group chondrites(L-chondrites) indicates that the shock metamorphism of H-chondrites is relatively low (except for GRV 022469, they are all lower than S5). A scenario for the history of the H-chondrite parent body is proposed that suggests the duration of the shock events in the H-chondrite parent bodies was much shorter than those in L-chondrite parent bodies. Also, the pressure may have been released more quickly, and consequently, the high-pressure phases should be easily preserved. However, the parent bodies of the H-chondrites may have been exposed to high temperatures for a longer time after the shock event, so the high-pressure phases formed by solid transformation might have retro-metamorphosed to low-pressure ones; its peak pressure is estimated to be less than 15 GPa. Wadsleyite was found in a shock vein in GRV022469, as confirmed by the Raman spectrometer. Petrological and mineralogical characteristics support the idea that the wadsleyite was formed by solid-state transformation.