Some adaptive image interpolation methods have been proposed to create higher visual quality images than traditional interpolation methods such as bicubic interpolation. These methods, however, often suffer from high computational costs and unnatural texture interpolation. This paper proposes a novel edge-adaptive image interpolation method using an edge-directed smoothness filter. Our approach estimates the enlarged image from the original image based on an observation model. The estimated image is constrained to have many edge-directed smooth pixels which are measured by using the edge-directed smoothness filter introduced in this paper. Simulation results show that the proposal method produces images with higher visual quality, higher PSNRs and faster computational times than the conventional methods.