This paper proposes a new method that reduces the computational cost of the phase-only correlation (POC)-based methods for displacement estimation in old film sequences. Conventional POC-based methods calculate all the points of the POC and only use the highest peak of the POC and its neighboring points to estimate the displacement with subpixel accuracy. Our proposed method reduces the computational cost by calculating the POC in a small region, instead of all the points of the POC. The proposed method combines a displacement pre-estimation with a modified inverse discrete Fourier transform (IDFT). The displacement pre-estimation uses the 1-D POCs of frame projections to pre-estimate the displacement with pixel accuracy and chooses a small region in the POC including the desired points for displacement estimation. The modified IDFT is then used to calculate the points in this small region for displacement estimation. Experimental results show that use of the proposed method can effectively reduce the computational cost of the POC-based methods without compromising the accuracy.