image can be represented with different formats, such as the equirectangular projection (ERP) image, viewport images or spherical image, for its different processing procedures and applications. Accordingly, the 360-degree image quality assessment (360-IQA) can be performed on these different formats. However, the performance of 360-IQA with the ERP image is not equivalent with those with the viewport images or spherical image due to the over-sampling and the resulted obvious geometric distortion of ERP image. This imbalance problem brings challenge to ERP image based applications, such as 360-degree image/video compression and assessment. In this paper, we propose a new blind 360-IQA framework to handle this imbalance problem. In the proposed framework, cubemap projection (CMP) with six inter-related faces is used to realize the omnidirectional viewing of 360-degree image. A multi-distortions visual attention quality dataset for 360-degree images is firstly established as the benchmark to analyze the performance of objective 360-IQA methods. Then, the perception-driven blind 360-IQA framework is proposed based on six cubemap faces of CMP for 360-degree image, in which human attention behavior is taken into account to improve the effectiveness of the proposed framework. The cubemap quality feature subset of CMP image is first obtained, and additionally, attention feature matrices and subsets are also calculated to describe the human visual behavior. Experimental results show that the proposed framework achieves superior performances compared with state-of-the-art IQA methods, and the cross dataset validation also verifies the effectiveness of the proposed framework. In addition, the proposed framework can also be combined with new quality feature extraction method to further improve the performance of 360-IQA. All of these demonstrate that the proposed framework is effective in 360-IQA and has a good potential for future applications.