Scattered x-rays are detrimental to the image quality of x-ray transmission radiography. Anti-scatter grids have been developed for kilovoltage (kV) x-ray imaging but are impractical to use for megavoltage (MV) x-ray imaging in radiation therapy. Our goal is to develop a new approach that uses an inherent anti-scatter detector for scatter reduction in MV x-ray imaging. A Monte Carlo simulation has been conducted to evaluate the response of a recently proposed Čerenkov electronic portal imaging device (CPID) to scattered x-rays. The proposed detector consists of a matrix of optical fibers aligned with the incident x-rays and coupled to an active matrix flat panel imager for image readout. The effects of scatter on the signal and noise of the CPID in comparison with those of conventional electronic portal imaging devices (EPIDs) have been investigated. It has been found that the CPID is ∼50% less sensitive to scattered x-rays than conventional EPIDs at 6 MV. The differential signal to noise ratio is also improved by up to 30% in the CPID. The results of our simulations have demonstrated that the recently proposed CPID system is an inherent anti-scatter detector, the first of this kind, for MV x-ray imaging.