The in-orbit performance and calibration of the Hard X-ray Detector (HXD) on board the X-ray astronomy satellite Suzaku are described. Its basic performances, including a wide energy bandpass of 10-600keV, energy resolutions of similar to 4 keV (FWHM) at 40 keV and similar to 11% at 511 keV, and a high background rejection efficiency, have been confirmed by extensive in-orbit calibrations. The long-term gains of PIN-Si diodes have been stable within 1% for half a year, and those of scintillators have decreased by 5-20%. The residual non-X-ray background of the HXD is the lowest among past non-imaging hard X-ray instruments in energy ranges of 15-70 and 150-500 keV. We provide accurate calibrations of energy responses, angular responses, timing accuracy of the HXD, and relative normalizations to the X-ray CCD cameras using multiple observations of the Crab Nebula.