In this letter, we propose a minimum BER (MBER) power allocation (PA) method for generalized frequency division multiplexing (GFDM) systems with zero forcing receiver. The MBER PA of GFDM systems is solved through minimizing noise enhancement factor at the receiver. Additionally, theoretical BER and achievable rate (AR) expressions are derived with the proposed PA strategy. Furthermore, we also generalize the MBER PA strategy in space-time coded (STC) GFDM systems. Simulation results show that, no matter GFDM or STC GFDM systems, the proposed PA strategy could improve BER and AR performances simultaneously.