Quadrature Amplitude Modulation based Filter-Bank Multi-Carrier (QAM-FBMC) is a promising technology to replace Orthogonal Frequency Division Multiplexing (OFDM) in future radio access systems. In this letter, we derive a bit error probability expression of QAM-FBMC systems over AWGN channels and over Rayleigh fading channels. We model the intrinsic interference related to the prototype filter through the interference table and consider the interference distribution to derive the bit error probability in QAM-FBMC systems. Numerical results reveal that the proposed expressions pair perfectly with the simulation results.