Abstract This paper presents a novel interpolation approach for single image super-resolution based on ordinary Kriging interpolation, which has been widely used in geostatistics. The proposed method simultaneously considers the intensity distances and geometry of the pixel data. We employ a new intensity distance definition and local windows surrounding each unknown high-resolution pixel to implement the algorithm. The proposed approach is able to produce adaptive weights and edge preservation is achieved. Our experimental results show the efficiency of the proposed approach compared to conventional interpolation methods in terms of the peak signal-to-noise (PNSR) and visual perception.