We capture 87Rb atoms from room-temperature background vapor with a magneto-optical trap (MOT). The temperature of the atoms in the MOT is 320 μK as the result of Doppler cooling. We further employ polarization gradient cooling to lower atom temperature. The factors that can affect the performance of polarization gradient cooling have been systematically studied. An atom temperature of 75 μK has been reached with the optimized conditions. Temperatures are measured by the release and recapture method and the time of flight method. Such cold atoms are ready for the evaporative cooling which will finally realize the Bose-Einstein condensation.