Abstract: The performance of codebooks designed for LSP with GLA and stochastic relaxation(SR) algorithm is investigated, and the features of two algorithms are discussed. The first order moving average prediction residual vectors of the mean removing LSP is used as the training sequence. The SR algorithm applied is a simplified SR algorithm for the decoder perturbation. The traditional conclusion is that SR saves GLA 1 bit per vector index. The experiment shows that the conclusion is right for a small amount of training sequence, but the difference in their performances is slight for a large amount of training sequence. The SNR improvement of codebook designed with SR algorithm is little when a LSP quantizer is designed.