CT scan by use of a beam filter placed between the x-ray source and the patient allows a single-scan low-dose dual-energy imaging with a minimal hardware modification to the existing CT systems. We have earlier demonstrated the feasibility of such an imaging method with a multi-slit beam filter reciprocating along the direction perpendicular to the CT rotation axis in a cone-beam CT system. However, such method would face mechanical challenges when the beam filter is supposed to cooperate with a fast-rotating gantry in a diagnostic CT system. Increasing penumbra effects of the beam-filter edges would also add an additional burden. In this work, we propose a new scanning method and associated image reconstruction algorithm that can overcome these challenges. We propose to slide a beam filter that has multi-slit structure with the slits being at a slanted angle with the CT gantry rotation axis during a scan. A streak pattern would be created in the sinogram domain as a result. Using a notch filter in the Fourier domain of the sinogram, we removed the streaks and reconstructed an image by use of the filtered-backprojection algorithm. The remaining image artifacts were suppressed by applying l0 norm based smoothing. Using this image as a prior, we have reconstructed low- and high-energy CT images in the iterative reconstruction framework. An image-based material decomposition then followed. We conducted a simulation study to test its feasibility using the XCAT phantom, and showed a successful material decomposition.