One well-recognized challenge of cone-beam computed tomography (CBCT) is the presence of scatter contamination within the projection images. Scatter degrades the CBCT image quality by decreasing the contrast, introducing shading artifacts and leading to inaccuracies in the reconstructed CT number. We propose a blocker-based approach to simultaneously estimate scatter signal and reconstruct the complete volume within the field of view (FOV) from a single CBCT scan. A physical strip attenuator (i.e., "blocker"), consists of lead strips, is inserted between the x-ray source and the patient. The blocker moves back and forth along z-axis during the gantry rotation. The two-dimensional (2D) scatter fluence is estimated by interpolating the signal from the blocked regions. A modified Feldkamp-Davis-Kress (FDK) algorithm and an iterative reconstruction based on the constraint optimization are used to reconstruct CBCT images from un-blocked projection data after the scatter signal is subtracted. An experimental study is performed to evaluate the performance of the proposed scatter correction scheme. The scatter-induced shading/cupping artifacts are substantially reduced in CBCT using the proposed strategy. In the experimental study using a CatPhan®600 phantom, CT number errors in the selected regions of interest are reduced from 256 to less than 20. The proposed method allows us to simultaneously estimate the scatter signal in projection data, reduce the imaging dose and obtain complete volumetric information within the FOV.