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Cooper minimum structure of high-order harmonic spectra from atoms or molecules has been extensively studied. In this paper, we demonstrate that the crystal harmonic spectra from an ultrashort mid-infrared laser pulse also exhibit the Cooper minimum characteristic. Based on the accurate band dispersion and k-dependent transition dipole moment (TDM) from the first-principle calculations, it can be found that the harmonic spectra from MgO crystal along {\Gamma}-X direction present a dip structure in the plateau, which is originated from the valley of TDM by examining the distribution of the harmonic intensity at the k-space. The Cooper minimum feature in crystal HHG will pave a new way to retrieve the band information of solid materials by using HHG from the ultrashort mid-infrared laser pulse., Comment: 6 pages, 8 figures