Cone beam computed tomography (CBCT) imaging is a key step in image guided radiation therapy (IGRT) to improve tumor targeting. The quality and imaging dose of CBCT are two important factors. However, X-ray scatter in the large cone beam field usually induces image artifacts and degrades the image quality for CBCT. A synchronized moving grid (SMOG) approach has recently been proposed to resolve this issue and shows great promise. However, the SMOG technique requires two projections in the same gantry angle to obtain full information due to signal blockage by the grid. This study aims to develop an inter-projection interpolation (IPI) method to estimate the blocked image information. This approach will require only one projection in each gantry angle, thus reducing the scan time and patient dose. IPI is also potentially suitable for sparse-view CBCT reconstruction to reduce the imaging dose. To be compared with other state-of-the-art spatial interpolation (called inpainting) methods in terms of signal-to-noise ratio (SNR) on a Catphan and head phantoms, IPI increases SNR from 15.3dB and 12.7dB to 29.0dB and 28.1dB, respectively. The SNR of IPI on sparse-view CBCT reconstruction can achieve from 28dB to 17dB for undersample projection sets with gantry angle interval varying from 1 to 3 degrees for both phantoms.