We report the experimental achievement of 87 Rb Bose-Einstein condensation in a magnetic trap with microwave and radio frequency (RF) induced evaporation. Evaporative cooling is realized by using 6.8 GHz microwave radiation driving the 87 Rb atoms to transit from the ground-state hyperfine state |F = 2, mF = 2 to |F = 1, mF = 1 . Compared with RF-induced evaporation, 87 Rb atoms are hardly to achieve pure condensate by microwave evaporation cooling due to the effect of atoms in the |F = 1, mF = 1 state being pumped back into the trapping |F = 2, mF = 1 state.