Deep convolution neural network (CNN) is one of the most popular Deep neural networks (DNN). It has won state-of-the-art performance in many computer vision tasks. The most used method to train DNN is Gradient descent-based algorithm such as Backpropagation. However, backpropagation algorithm usually has the problem of gradient vanishing or gradient explosion, and it relies on repeated iteration to get the optimal result. Moreover, with the need to learn many convolutional kernels, the traditional convolutional layer is the main computational bottleneck of deep CNNs. Consequently, the current deep CNN is inefficient on computing resource and computing time. To solve these problems, we proposed a method which combines Gabor kernel, random kernel and pseudoinverse kernel, incorporating with pseudoinverse learning (PIL) algorithm to speed up DNN training processing. With the multiple fixed convolution kernels and pseudoinverse learning algorithm, it is simple and efficient to use the proposed method. The performance of the proposed model is tested on MNIST and CIFAR-10 datasets without using GPU. Experimental results show that our model is better than existing benchmark methods in speed, at the same time it has the comparative recognition accuracy.