This paper proposes a novel method to estimate non-integer shift of images based on least squares approximation in the phase region. Conventional methods based on Phase Only Correlation (POC) take correlation between an image and its shifted image, and then estimate the non-integer shift by fitting the model equation. The problem when estimating using POC is that the estimated peak of the fitted model equation may not match the true peak of the POC function. This causes error in non-integer shift estimation. By calculating the phase difference directly in the phase region, the proposed method allows the estimation of sub-pixel shift through least squares approximation. Also by utilizing the characteristics of natural images, the proposed method limits adoption range for least squares approximation. By these improvements, the proposed method achieves high accuracy, and we validate through some examples.