Imperfections in quadrature modulators (QMs), such as inphase and quadrature (IQ) imbalance, can severely impact the performance of power amplifier (PA) linearization systems, in particular in adaptive digital predistorters (PDs). In this paper, we first analyze the effect of IQ imbalance on the performance of a memory orthogonal polynomials predistorter (MOP PD), and then we propose a new adaptive algorithm to estimate and compensate the unknown IQ imbalance in QM. Unlike previous compensation techniques, the proposed method was capable of online IQ imbalance compensation with faster convergence, and no special calibration or training signals were needed. The effectiveness of the proposed IQ imbalance compensator was validated by simulations. The results clearly show the performance of the MOP PD to be enhanced significantly by adding the proposed IQ imbalance compensator.