To achieve good reconstruction speech quality in a very low bit rate speech codecs, an efficient dimension reduction quantization scheme for the linear spectrum pair (LSP) parameters is proposed based on compressed sensing (CS). In the encoder, the LSP parameters extracted from consecutive speech frames are shaped into a high dimensional vector, and then the dimension of the vector is reduced by CS to produce a low dimensional measurement vector, the measurements are quantized using the split vector quantizer. In the decoder, according to the quantized measurements, the original LSP vector is reconstructed by the orthogonal matching pursuit method. Experimental results show that the scheme is more efficient than that of conventional matrix quantization scheme, the average spectral distortion reduction of up to 0.23dB is achieved in the DFT transform domain. Moreover, in the approximate KLT transform domain, this scheme can obtain transparent quality at 5 bits/frame with drastic bits reduction compared to other methods.