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This paper proposes a new method for vector quantization (VQ) of LSP parameters, using moving average (MA) interframe predictions. MA predictive VQ executes the prediction using the code vectors (codebook outputs) in the previous frames. Moreover, this method has the following features, compared to autoregressive (AR) predictive coding, which executes the prediction based on the previous quantized (decoded) values: (1) even if a bit error is produced in the transmission channel, its effect to the succeeding frames remains finite; and (2) the stored codes can be decoded from any time point. This paper discusses the quantization performance and the robustness against bit errors of the MA predictive VQ, as well as the training method for the codebook. Assuming an application to low‐bit‐rate speech coding, the configuration considered has a frame length of 40 ms, with each frame composed of four subframes. A method for further improvement of the efficiency is reported. As a result of evaluation using actual speech data, bit reductions of approximately 16 percent and 23 percent are achieved for the quantization for each 20 ms and 40 ms, respectively, compared to the conventional method which does not use interframe prediction.