We propose a new frame rate up-conversion (FRC) algorithm using the adaptive motion compensation (MC) that reduces the blocking artifacts due to block-based processing. In the proposed scheme, after conventional motion estimation (ME) between two adjacent frames is performed to construct the motion vectors for the frame to be interpolated, the motion analysis is used to determine the type of motion and the motion-compensated interpolation (MCI) is applied adaptively. Unlike conventional MCI algorithms, the proposed technique utilizes similar neighboring motion vectors to produce multiple motion trajectories. When the proposed MCI is applied, multiple motion trajectories are considered in order to increase the accuracy of the MCI. The proposed method provides high quality format conversion with significantly reduced blocking artifacts.