Non-hydrostatic stresses of KBr acting as a pressure-transmitting medium have been investigated by examining their effect on a single crystal of quartz in a diamond anvil cell (DAC). The lattice strains or distortions were measured by single-crystal x-ray diffraction methods, and the non-hydrostatic deviatoric stresses for KBr were determined up to 5.63(2) GPa. The experimental results show that differences between axial stress components in the direction normal to the DAC culet face and the radial stress components in directions parallel to the DAC culet face are about 0.063(24) GPa at pressures below 2.14 GPa, and the pressure-transmitting medium can therefore be considered as quasi-hydrostatic up to this pressure. However above 2.14 GPa, after the phase transition pressure of KBr during which it converts from the B1 phase to the B2 phase, the deviatoric stresses constantly increase with increasing pressure. At the maximum pressure of this study, 5.63(2) GPa, the difference between axial stress and radial stress components reaches 0.93(9) GPa. Different variations in the non-hydrostatic deviatoric stresses were observed during both compression and decompression of the DAC, and are mainly ascribed to the phase-transition-induced volume change of KBr.