This paper proposes the speech and noise recognition system by using a neural network in order to detect the speech and noise sections at each frame. The proposed neural network consists of a layered neural network training by back-propagation algorithm. First, a power spectrum obtained by fast Fourier transform and linear predictive coefficients are used as the input to the neural network for each frame, then the neural network is trained using these power spectrum and linear predictive coefficients. Therefore, the proposed neural network can train using clean speech and noise. The performance of the proposed recognition system was evaluated based on the recognition rate using various speeches and white, printer, road, and car noises. In this experiment, the recognition rates were 92% or more for such speech and noise when training data and evaluation data were the different.