Cone-beam CT (CBCT) is being increasingly used in modern radiation therapy for patient setup and adaptive replanning. However, due to the large volume of x-ray illumination, scatter becomes a rather serious problem and is considered as one of the fundamental limitations of CBCT image quality. Many scatter correction algorithms have been proposed in literature, while a standard practical solution still remains elusive. In radiation therapy, the same patient is scanned repetitively during a course of treatment, a natural question to ask is whether one can obtain the scatter distribution on the first day of treatment and then use the data for scatter correction in the subsequent scans on different days. To realize this scatter removal scheme, two technical pieces must be in place: (i) A strategy to obtain the scatter distribution in on-board CBCT imaging and (ii) a method to spatially match a prior scatter distribution with the on-treatment CBCT projection data for scatter subtraction. In this work, simple solutions to the two problems are provided. A partially blocked CBCT is used to extract the scatter distribution. The x-ray beam blocker has a strip pattern, such that partial volume can still be accurately reconstructed and the whole-field scatter distribution can be estimated from the detected signals in the shadow regions using interpolation/extrapolation. In the subsequent scans, the patient transformation is determined using a rigid registration of the conventional CBCT and the prior partial CBCT. From the derived patient transformation, the measured scatter is then modified to adapt the new on-treatment patient geometry for scatter correction. The proposed method is evaluated using physical experiments on a clinical CBCT system. On the Catphan 600 phantom, the errors in Hounsfield unit (HU) in the selected regions of interest are reduced from about 350 to below 50 HU; on an anthropomorphic phantom, the error is reduced from 15.7% to 5.4%. The proposed method is attractive in applications where a high CBCT image quality is critical, for example, dose calculation in adaptive radiation therapy.