Traditional algorithms can result in the blurring or zigzag on edges in the image zooming. A new method for image zooming is presented which focuses on the triangulation of the pixels in the rectangle mesh. The accessorial control points associated with the undetermined curves can be presented by the position and distance of the interrelated pixels. The Bézier curves, which interpolate the accessorial control points, are used to construct the Coons surface via boundary. The new method can preserve and intensify the edge characters of the image. Especially, the edge characters in the gradient or sharp-angled area can be preserved better.