In recent years, intelligent fault diagnosis algorithms using deep learning method have achieved much success. However, the signals collected by sensors contain a lot of noise, which will have a great impact on the accuracy of the diagnostic model. To address this problem, we propose a one-dimensional convolutional neural network with multi-scale kernels (MSK-1DCNN) and apply this method to bearing fault diagnosis. We use a multi-scale convolution structure to extract different fault features in the original signal, and use the ELU activation function instead of the ReLU function in the multi-scale convolution structure to improve the anti-noise ability of MSK-1DCNN; then we use the training set with pepper noise to train the network to suppress overfitting. We use the Western Reserve University bearing data to verify the effectiveness of the algorithm and compare it with other fault diagnosis algorithms. Experimental results show that the improvements we proposed have effectively improved the diagnosis performers of MSK-1DCNN under strong noise and the diagnosis accuracy is higher than other comparison algorithms.