Due to the subjective nature of image quality assessment (IQA), assessing which image has better quality among a sequence of images is more reliable than assigning an absolute mean opinion score for an image. Thus, IQA models are evaluated by global correlation consistency (GCC) metrics like PLCC and SROCC, rather than mean opinion consistency (MOC) metrics like MAE and MSE. However, most existing methods adopt MOC metrics to define their loss functions, due to the infeasible computation of GCC metrics during training. In this work, we construct a novel loss function and network to exploit Global-correlation and Mean-opinion Consistency, forming a GMC-IQA framework. Specifically, we propose a novel GCC loss by defining a pairwise preference-based rank estimation to solve the non-differentiable problem of SROCC and introducing a queue mechanism to reserve previous data to approximate the global results of the whole data. Moreover, we propose a mean-opinion network, which integrates diverse opinion features to alleviate the randomness of weight learning and enhance the model robustness. Experiments indicate that our method outperforms SOTA methods on multiple authentic datasets with higher accuracy and generalization. We also adapt the proposed loss to various networks, which brings better performance and more stable training.