Magnetic resonance (MR) image acquisition is an inherently prolonged process, whose acceleration has long been the subject of research. This is commonly achieved by obtaining multiple undersampled images, simultaneously, through parallel imaging. In this paper, we propose the Dual-Octave Network (DONet), which is capable of learning multi-scale spatial-frequency features from both the real and imaginary components of MR data, for fast parallel MR image reconstruction. More specifically, our DONet consists of a series of Dual-Octave convolutions (Dual-OctConv), which are connected in a dense manner for better reuse of features. In each Dual-OctConv, the input feature maps and convolutional kernels are first split into two components (ie, real and imaginary), and then divided into four groups according to their spatial frequencies. Then, our Dual-OctConv conducts intra-group information updating and inter-group information exchange to aggregate the contextual information across different groups. Our framework provides three appealing benefits: (i) It encourages information interaction and fusion between the real and imaginary components at various spatial frequencies to achieve richer representational capacity. (ii) The dense connections between the real and imaginary groups in each Dual-OctConv make the propagation of features more efficient by feature reuse. (iii) DONet enlarges the receptive field by learning multiple spatial-frequency features of both the real and imaginary components. Extensive experiments on two popular datasets (ie, clinical knee and fastMRI), under different undersampling patterns and acceleration factors, demonstrate the superiority of our model in accelerated parallel MR image reconstruction.