A vector quantization method using statistics, i.e., mean and covariance, of neighboring input vectors (or linear transform of those) is proposed. In the proposed method, the distance between the input vector and the codeword is measured by the output probability defined by the statistics, and the output vector sequence is determined so that the output probability of the output vector sequence is maximized. The codebook can be trained by a conventional training procedure based on the statistically defined distance or a simplified distance. The value of the output vector sequence is determined by a high-order set of equations. Fortunately, it can be shown that the set of equations can be solved by a fast algorithm. In the conventional vector quantization methods, adjoining output vectors can change discontinuously; quantizing speech spectral parameter vectors causes perceivable glitches in the synthesized speech, whereas, in the proposed method, the change of adjoining output vectors is controlled appropriately according to the statistics of neighboring input vectors. Through an example of vector quantization of the LSP coefficients obtained from natural speech, it is shown that the proposed method can improve objective and subjective performance of vector quantization.