The nonrelativistic and relativistic full-configuration-interaction calculations are performed for the low-lying triplet states of Be2+ ion. The energies for n3S1, n3PJ and n3DJ states, and the dipole oscillator strengths for the 23S1(33S1)→n3PJ and 23PJ(33PJ)→n3DJ transitions with the main quantum number n up to 5 are determined. We calculate the nonrelativistic dynamic dipole polarizabilities by using the sum rule of intermediate states. In addition, the tune-out wavelengths for the four lowest triplet states and magic wavelengths for the 23S→23P and 23S→33P transitions are obtained.