Objective. This study aims at developing a simple and rapid Compton scatter correction approach for cone-beam CT (CBCT) imaging. Approach. In this work, a new Compton scatter estimation model is established based on two distinct CBCT scans: one measures the full primary and scatter signals without anti-scatter grid (ASG), and the other measures a portion of primary and scatter signals with ASG. To accelerate the entire data acquisition speed, a half anti-scatter grid (h-ASG) that covers half of the full detector surface is proposed. As a result, the distribution of scattered x-ray photons could be estimated from a single CBCT scan. Physical phantom experiments are conducted to validate the performance of the newly proposed scatter correction approach. Main results. Results demonstrate that the proposed half grid approach can quickly and precisely estimate the distribution of scattered x-ray photons from only one single CBCT scan, resulting in a significant reduction of shading artifacts. In addition, it is found that the h-ASG approach is less sensitive to the grid transmission fractions, grid ratio and object size, indicating a robust performance of the new method. Significance. In the future, the Compton scatter artifacts can be quickly corrected using a half grid in CBCT imaging.