Magnetic resonance imaging (MRI) is widely employed for diagnostic tests in neurology. However, the utility of MRI is largely limited by its long acquisition time. Acquiring fewer k-space data in a sparse manner is a potential solution to reducing the acquisition time, but it can lead to severe aliasing reconstruction artifacts. In this paper, we present a novel Dual-Domain Cross-Iteration Squeeze and Excitation Network (DD-CISENet) for accelerated sparse MRI reconstruction. The information of k-spaces and MRI images can be iteratively fused and maintained using the Cross-Iteration Residual connection (CIR) structures. This study included 720 multi-coil brain MRI cases adopted from the open-source fastMRI Dataset. Results showed that the average reconstruction error by DD-CISENet was 2.28 $\pm$ 0.57%, which outperformed existing deep learning methods including image-domain prediction (6.03 $\pm$ 1.31, p < 0.001), k-space synthesis (6.12 $\pm$ 1.66, p < 0.001), and dual-domain feature fusion approaches (4.05 $\pm$ 0.88, p < 0.001).