Many adaptive gradient methods have been successfully applied to train deep neural networks, such as Adagrad, Adadelta, RMSprop and Adam. These methods perform local optimization with an element-wise scaling learning rate based on past gradients. Although these methods can achieve an advantageous training loss, some researchers have pointed out that their generalization capability tends to be poor as compared to stochastic gradient descent (SGD) in many applications. These methods obtain a rapid initial training process but fail to converge to an optimal solution due to the unstable and extreme learning rates. In this paper, we investigate the adaptive gradient methods and get the insights on various factors that may lead to poor performance of Adam. To overcome that, we propose a bounded scheduling algorithm for Adam, which can not only improve the generalization capability but also ensure the convergence. To validate our claims, we carry out a series of experiments on the image classification and the language modeling tasks on several standard benchmarks such as ResNet, DenseNet, SENet and LSTM on typical data sets such as CIFAR-10, CIFAR-100 and Penn Treebank. Experimental results show that our method can eliminate the generalization gap between Adam and SGD, meanwhile maintaining a relative high convergence rate during training.