This paper proposes a method of low complexity speech mixing with speech codecs based on predictive coding for multimedia conferences. The proposed method applies a filter state management (FSM) technique to a partial mixing method in order to avoid inconsistency of the filter states of encoders. The inconsistency is created by switching of the encoders when the speakers to be mixed are switched. The results of subjective evaluations of speech quality show that the proposed method avoids the inconsistency, and achieves significantly higher speech quality than the conventional partial mixing method without the FSM and almost the same speech quality as the full mixing method. The complexity evaluation results show that the proposed method achieves much lower complexity than the full mixing method.