To further meet the large capacity, high spectrum efficiency (SE), reduce the signal-signal beat interference (SSBI) of the independent dual single sideband (ISB) system and the complexity of the receiver, we propose an iterative signal-signal beat interference counteraction (ISSBIC) algorithm to suppress SSBI. The 16-Gbps left sideband and the 16-Gbps right sideband signals in the ISB system are quadrature phase-shift keying (QPSK) modulated. After standard single-mode fiber (SSMF) transmission, the LSB and RSB signals are synthesized to a 16-quadrature amplitude modulation (QAM) signal after conversion through the photodetector (PD) square law. The simulation results show that the ISSBIC with just 2 iterations is superior to Kramers-Kronig (KK) receiver in processing the system error bit. In the meantime, the ISSBIC requires a sampling rate of 20GSa/s, whereas KK requires 40GSa/s. Moreover, the proposed ISSBIC algorithm has a simpler complexity. According to the simulation results, the suggested ISSBIC receiver can lower the ADC requirements and system costs, which opens up a wide range of applications in multiplex and higher SE transmission systems.