In this paper, we have proposed MIMO-IBFD system that can transmit and receive multiple data stream at the same time in the single band, and analyze the system. We have confirmed that MIMO-IBFD system requires multiple RF cancellation and multiple Digital cancellation techniques. In simulation, we have analyzed characteristic of received signal on MIMO-IBFD system, and evaluate system performance of conventional 2x2 MIMO system and MIMO-IBFD system. As simulation results, we have confirmed that MIMO-IBFD system can transmit and receive multiple data stream at the same time in the single band by using multiple RF and digital cancellation techniques. Additionally, we have confirmed that BER performance of 2x2 MIMO-IBFD system with low-level QAM modulation is similar to performance of 2x2 MIMO system, and BER performance of 2x2 MIMO-IBFD system with high-level QAM modulation is degraded in comparison with 2x2 MIMO system with high-level QAM modulation. We can confirm that MIMO-IBFD system requires high level self-interference cancellation technique in order to use high level modulation.