The quality of screen content images (SCIs) plays a crucial benchmark of displaying the system and directly affects the user experience of multidevice communication. However, accurately predicting the quality of SCIs with an objective algorithm still has many challenges. Hence, we propose a new no-reference method for evaluating the quality of SCIs effectively and efficiently. Specifically, we first propose a simple but effective strategy to partition the SCIs into the rough and smooth regions. Then, a most preferred structure (MPS) metric is derived to represent the meaningful part of each image patch according to the free-energy theory of human brain. Subsequently, the MPSs of the rough and smooth regions are pooled for constructing the rough and smooth features of SCIs, separately. Finally, to evaluate the final visual quality, the rough and smooth features are combined as the quality-aware features of SCIs, and a learning-based framework is employed to map the quality-aware features to objective quality scores. The experimental results show that the performance of the proposed method is highly consistent with the human perception and superior to the state-of-the-art quality assessment methods on the SCI-oriented databases. Furthermore, the proposed method delivers a high computational efficiency and is very suitable to be integrated into the displaying system.