This paper proposes an estimation method of frame displacement for old films using phase-only correlation. The displacement correction for old films needs the subpixel displacement estimation and correction for movie stabilization. Subpixel displacement in images is caused by sampling analog signals. For the estimation of the subpixel displacement, the quadratic curve fitting method is proposed. This method is based on approximating the phase-only correlation of two images by a sinc function. Experimental results show that the proposed method is useful for the estimation of the subpixel displacement and robust against noises peculiar to old films. Moreover, the method is applied to the frame displacement estimation for old films. It is shown that frame displacement of old films can be estimated accurately and then corrected. Visual inspection confirms that the proposed method can reduce the frame displacement significantly.