We report the experimental achievement of ⁸⁷Rb 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 ⁸⁷Rb atoms to transit from the ground-state hyperfine state |F = 2,mF =2> to |F = 1,mF = 1>. Compared with RF-induced evaporation, ⁸⁷Rb 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.