This paper addresses the performance of a full-duplex (FD) generalized frequency division multiplexing (GFDM) transceiver in the presence of radio frequency (RF) impairments including phase noise, carrier frequency offset (CFO) and in-phase (I) and quadrature (Q) imbalance. We study analog and digital self-interference (SI) cancellation and develop a complementary SI suppression method. Closed-form solutions for the residual SI power and the desired signal power and signal-to-interference ratio (SIR) are provided. Simulation results show that the RF impairments degrade SI cancellation and FD GFDM is more sensitive to them compares to FD orthogonal frequency division multiplexing (OFDM). Hence, we propose an FD GFDM receiver filter for maximizing the SIR. Significantly, it achieves 25 dB higher SIR than FD OFDM transceiver.