A disclosed pixel interpolation apparatus for converting an image to a predetermined resolution includes a first interpolating part configured to calculate a first interpolation pixel value by performing high order interpolation using pixel values of plural first reference pixels and a distance between the plural first reference pixels and a first interpolation pixel; a second interpolating part configured to calculate a second interpolation pixel value by performing weighted interpolation using pixel values of plural second reference pixels, an edge gradient of the second reference pixels, and the distance between the second reference pixels and a second interpolation pixel; an overshoot area detecting part configured to detect an overshoot area in the image; and an interpolation pixel selecting part configured to determine whether to perform the high order interpolation or the weighted interpolation according to a detection result of the overshoot area detecting part.