Multi-spectral imaging technologies have made great progress in the past few decades. The development of snapshot cameras equipped with a specific multi-spectral filter array (MSFA) allow dynamic scenes to be captured on a miniaturized platform across multiple spectral bands, opening up extensive applications in quantitative and visualized analysis. However, a snapshot camera based on MSFA captures a single band per pixel; thus, the other spectral band components of pixels are all missed. The raw images, which are captured by snapshot multi-spectral imaging systems, require a reconstruction procedure called demosaicing to estimate a fully defined multi-spectral image (MSI). With increasing spectral bands, the challenge of demosaicing becomes more difficult. Furthermore, the existing demosaicing methods will produce adverse artifacts and aliasing because of the adverse effects of spatial interpolation and the inadequacy of the number of layers in the network structure. In this paper, a novel multi-spectral demosaicing method based on a deep convolution neural network (CNN) is proposed for the reconstruction of full-resolution multi-spectral images from raw MSFA-based spectral mosaic images. The CNN is integrated with the channel attention mechanism to protect important channel features. We verify the merits of the proposed method using 5 x 5 raw mosaic images on synthetic as well as real-world data. The experimental results show that the proposed method outperforms the existing demosaicing methods in terms of spatial details and spectral fidelity.