An input speech signal is encoded by an adaptive quantizer which quantizes the predicted residual signal between the digital input speech signal, and prediction signals provided by predictors and a shaped quantization noise provided by a noise shaping filter. An inverse quantizer, to which the encoded speech signal is supplied, is provided for noise shaping and local decoding. A noise shaping filter makes the spectrum of the quantization noise similar to that of the original digital input speech signal by using the shaping factors. The shaping factors are changed depending upon the prediction gain (ex. ratio of input speech signal to predicted residual signal or the prediction coefficients). On a decoding side of the system there are an inverse quantizer, predictors, and a post noise shaping filter. The shaping factors for the post noise shaping filter are similarly changed depending upon the prediction gain.