This paper presents a robust timing synchronization method for full duplex orthogonal frequency division multiplexing (OFDM) systems based on Long Term Evolution (LTE). The proposed method contains two essential steps: 1) time alignment between the desired signal and self-interference 2) normalized synchronization peak (NSP) index switching. The time alignment is to make the difference in arrival times of the desired signal and the self-interference signal within cyclic prefix (CP) duration of an OFDM symbol, exploiting a time advance, thereby adopting low-complexity, frequency domain self-interference cancellation and decoding. In the second step, to improve the probability of successful time synchronization, a Zadoff-Chu sequence with a different root index is used for the primary synchronization signal at each node. To validate the proposed method with experimental evidence, we implement a full duplex physical layer (PHY) on an FPGA-based software-defined radio (SDR) platform. It is shown that our full duplex OFDM synchronizer is flexible and robust, in a real-world wireless channel, compared to existing synchronization method.