Abstract: The theory of Linear Prediction (LP) of speech wave is summerized in this paper, especially on autocorrelation LP method and selective LP method. The iterative solution process of autocorrelation normal equation is presented. It is pointed out that the selective LP method has special applications in specific problems such as speech recognition. Some new basic parameters and calculations used for speech recognition are presented. It is emphasized that the LP parameters are quite sueful in Vocodic speech recognition. The other applications of LP such as Formant extraction and pitch detection of voiced speech are also pointed out.