In the intelligent fault diagnosis of rolling bearings, the high recognition accuracy is hardly achieved when small training samples and strong noise happen. In this article, a novel fault diagnosis method is proposed, that is radial basis function neural network with power spectrum of Welch method. This fault diagnosis model adopts the way of end-to-end operating mode. It takes the original vibration signal (time-domain signal) as input, and Welch method transforms the data from time-domain signals to power spectrums and suppresses high strength noise. Then the results of Welch method are classified by radial basis function neural network. To test the performance of radial basis function neural network with power spectrum of Welch method, the method is compared with some advanced fault diagnosis methods, and the limit performance test for radial basis function neural network with power spectrum of Welch method is carried out to obtain its ultimate diagnosis ability. The results show that the proposed method can realize the high diagnostic precision without the complex feature extraction from the signal. At the same time, in the case of a small amount of training data, this method also can achieve the diagnosis in high precision. Moreover, the anti-noise performance of radial basis function neural network with power spectrum of Welch method is better than the performance of some fault diagnosis methods proposed in recent years.