The method of spectrum analysis by using neural network algorithm was presented. The convergence of the neural-network algorithm was studied. Simulation examples of spectrum analysis were given. The results show that the approaches of spectrum analysis presented in this study are not involved in plural multiplication operation and plural addition operation. The high accuracy and fast convergence speed are the features of the method presented in this study. Software and hardware of the approach are easily implemented. It is especially fit for the implementation of software and hardware about DSP. Therefore, the methods of spectrum analysis proposed in this study are effective.