Distributed asynchronous offline training has received widespread attention in recent years because of its high performance on large-scale data and complex models. As data are distributed from cloud-centric to edge nodes, a big challenge for distributed machine learning systems is how to handle native and natural non-independent and identically distributed (non-IID) data for training. Previous asynchronous training methods do not have a satisfying performance on non-IID data because it would result in that the training process fluctuates greatly which leads to an abnormal convergence. We propose a gradient scheduling algorithm with partly averaged gradients and global momentum (GSGM) for non-IID data distributed asynchronous training. Our key idea is to apply global momentum and local average to the biased gradient after scheduling, in order to make the training process steady. Experimental results show that for non-IID data training under the same experimental conditions, GSGM on popular optimization algorithms can achieve a 20% increase in training stability with a slight improvement in accuracy on Fashion-Mnist and CIFAR-10 datasets. Meanwhile, when expanding distributed scale on CIFAR-100 dataset that results in sparse data distribution, GSGM can perform a 37% improvement on training stability. Moreover, only GSGM can converge well when the number of computing nodes grows to 30, compared to the state-of-the-art distributed asynchronous algorithms. At the same time, GSGM is robust to different degrees of non-IID data.