These authors contributed equally to this work. Abstract Training deep neural networks is a challenging task. In order to speed up training and enhance the performance of deep neural networks, we rectify the vanilla conjugate gradient as conjugate-gradient-like and incorporate it into the generic Adam, and thus propose a new optimization algorithm named CG-like-Adam for deep learning. Specifically, both the first-order and the second-order moment estimation of generic Adam are replaced by the conjugate-gradient-like. Convergence analysis handles the cases where the exponential moving average coefficient of the first-order moment estimation is constant and the first-order moment estimation is unbiased. Numerical experiments show the superiority of the proposed algorithm based on the CIFAR10/100 dataset. Introduction Deep learning has been used in many aspects, such as recommendation systems [1], natural language processing [2], image recognition [3], reinforcement learning [4], etc. Neural network model is the main research object of deep learning, which includes input layer, hidden layer and output layer. Each layer includes a certain number of neurons, and each neuron is connected with each other in a certain way. The parameters and connection parameters of each neuron determine the performance of the deep learning model.