We propose a numerical and automatic quadratic phase aberration elimination method in digital holography for phase-contrast imaging. A histogram segmentation method based on Gaussian 1σ-criterion is used to obtain the accurate coefficients of quadratic aberrations using the weighted least-squares algorithm. This method needs no manual intervention for specimen-free zone or prior parameters of optical components. We also propose a maximum-minimum-average-standard deviation (MMASD) metric to quantitatively evaluate the effectiveness of quadratic aberration elimination. Simulation and experimental results are demonstrated to verify the efficacy of our proposed method over the traditional least-squares algorithm.