Dual-energy CT (DECT) has better material discrimination capability than single-energy CT. In this paper, we propose a low-dose DECT scanning strategy with double scans under different energy spectra. In the strategy a low-energy scan is performed with a complete number of views, and the high-energy scan is in much sparser views to reduce radiation dose. In such conditions, the high-energy reconstruction image suffers from severe streak artifacts due to under-sampling. To address this problem a novel non-local image restoration method is proposed. Because the low and high energy scans are performed on the same object, the reconstructed images should have identical object structures. Therefore the low-energy reconstruction that comes from the complete scan may serve as a reference image to help improving the image quality of the high-energy reconstruction. The method is implemented with the following steps. First, the structure information is obtained by a non-local pixel similarity measurement on the low-energy CT image, and second after a registration between the high and low reconstructions the high-energy image is restored by normalized weighted average using the calculated similarity relationship. Compared with previous methods, the new method achieves better image quality in both structure preservation and artifact reduction. Besides, the computation is much cheaper than iterative reconstruction methods, which makes the method of practical value. Numerical and pre-clinical experiments have been performed to illustrate the effectiveness of the proposed method. With the novel DECT scanning configuration and non-local image restoration method, the total dose is significantly reduced while maintaining a high reconstruction quality.