Four dimensional (4D) X-ray cone-beam computed tomography (CBCT) can lead to a precise radiation therapy through accurate tumor motion modeling. However, the repeated use of 4D CBCT in a fractional treatment session raises the concern of radiation dose. In addition, the scatter contamination results in shading artifacts and low contrast in reconstructed images if not corrected. In this work, we propose a novel method to use a moving blocker (MB) to achieve the dose reduction and scatter correction simultaneously for 4D CBCT, termed 'MB4D'. The lead blocker is placed between the X-ray source and the patient and moving back and forth in a certain direction during the CBCT data collection. Not only is part of radiation blocked, but also the scatter signal can be estimated from the blocked region for scatter correction (SC). The spatial total variation (TV) minimization and motion correlations are used to improve 4D reconstruction with incomplete data and to derive the motion fields. As an initial test of this novel method, we used a simulation study using the 4D non-uniform rational B-spline cardiac-torso (NCAT) phantom. Our results show that with 1/3 dose reduction the proposed MB-4D method can achieve much better image quality than 3D reconstruction with SC ('MB-3D') and 4D reconstruction without SC ('4D'), measured by structural similarity (SSIM) index, root mean square error (RMSE) of CT numbers, and time attenuation coefficient (TAC) curves.