A novel perceptual postfilter is introduced. For each frame, the filter gains, z, are estimated given a vector, y, of the quantized LSFs and the long-term prediction gain of the corresponding frame. The proposed perceptual postfilter is derived from an optimal MMSE estimator, i.e. the estimated gain vector is ˆz = E{z|y}. The MMSE estimator is based on the conditional pdf of z given y, which is computed from the joint pdf modelled by a GMM. The proposed perceptual postfilter improves the speech naturalness comparing with the conventional adaptive postfilter, while maintaining the property of being an "add-on" postfilter without modification to the current encoder.