W/C and Co/SiO2 multilayer gratings have been fabricated by depositing a multilayer coating on the surface of laminar-type holographic master gratings. The diffraction efficiency was measured by reflectometers in the energy region of 0.6-8.0 keV at synchrotron radiation facilities as well as at an x-ray diffractometer at 8.05 keV. The Co/SiO2 and W/C multilayer gratings showed peak diffraction efficiencies of 0.47 and 0.38 at 4.0 and 8.0 keV, respectively. The peak efficiency of the Co/SiO2 multilayer grating is the highest measured with hard x-rays, to our knowledge. The diffraction efficiency of the Co/SiO2 multilayer gratings was higher than that of the W/C multilayer grating in the energy range of 2.5 6.0 keV. However, it decreased significantly in the energy above the K-absorption edge of Co (7.71 keV). For the Co/SiO2 multilayer grating the measured diffraction efficiencies agreed with the calculated curves assuming a rms roughness ~1 nm.