The aim of this thesis work is to investigate the algorithms of speech recognition. The author programmed and simulated the designed systems for algorithms of speech recognition in MATLAB. There are two systems designed in this thesis. One is based on the shape information of the cross-correlation plotting. The other one is to use the Wiener Filter to realize the speech recognition. The simulations of the programmed systems in MATLAB are accomplished by using the microphone to record the speaking words. After running the program in MATLAB, MATLAB will ask people to record the words three times. The first and second recorded words are different words which will be used as the reference signals in the designed systems. The third recorded word is the same word as the one of the first two recorded words. After recording words, the words will become the signals’ information which will be sampled and stored in MATLAB. Then MATLAB should be able to give the judgment that which word is recorded at the third time compared with the first two reference words according to the algorithms programmed in MATLAB. The author invited different people from different countries to test the designed systems. The results of simulations for both designed systems show that the designed systems both work well when the first two reference recordings and the third time recording are recorded from the same person. But the designed systems all have the defects when the first two reference recordings and the third time recording are recorded from the different people. However, if the testing environment is quiet enough and the speaker is the same person for three time recordings, the successful probability of the speech recognition is approach to 100%. Thus, the designed systems actually work well for the basical speech recognition.