We proposed a novel scanning method for low-dose computed tomography (CT) that uses an oscillating multi-slit collimator between the x-ray source and the patient. It can be thought as a realization of sparse data sampling that does not require a fast x-ray power switching. A simulation study was performed based on experimentally acquired microCT data of a mouse to demonstrate the feasibility of the proposed method. A numerical collimation was designed to leave only one-fourth of each projection data for use in image reconstruction. A total-variation minimization algorithm was implemented for image reconstruction from the sparely sampled data. We have successfully shown that the proposed method provides a viable option to low-dose CT.