In this paper, a low-complexity multi-dimensional architecture for IQ imbalance compensation is proposed, which reduces the effects of in-phase (I) and quadrature (Q) imbalance. The architecture use a transceiver IQ skew estimation structure to compensate for IQ skew, and then use a low-complexity MIMO equalizer to compensate for IQ amplitude/phase imbalance. In the transceiver IQ skew estimation structure, the receiver(RX) IQ skew is estimated by Gardner's phase detector, and the transmitter TX skew is estimated by finding the value that yields the lowest equalizer error. The low-complexity MIMO equalizer consists of a complex-valued MIMO (CV-MIMO) and a two-layer multimodulus algorithm real-valued MIMO (TMMA-RV-MIMO), which employ a butterfly and a non-butterfly structure, respectively. The CV-MIMO is used to perform polarization demultiplexing and the TMMA-RV-MIMO equalizes each of the two polarizations. In addition, the TMMA-RV-MIMO can recovery the carrier phase. A 100 km transmission simulation and experiment with 36 Gbaud dual-polarization 16 quadrature amplitude modulation (DP-16QAM) signals showed that, with the TX/RX IQ skew estimation, the estimation error is less than 0.9/0.25 ps. The low-complexity MIMO equalizer can tolerate 0.1 TX IQ amplitude imbalance and 5 degrees at a 0.3 dB Q-factor penalty. The number of real multiplications is reduced by 55% compared with conventional cases in total.