This study focuses on developing a pragmatic and robust method in the estimation of fracture orientation assuming a single set of aligned fractures. The Young’s modulus in the direction of fracture orientation is larger than that in the perpendicular direction that helps to solve the problem of the ambiguity in fracture-orientation estimation existing in the method of using the variation of amplitude-variation-with-offset (AVO) gradients with azimuth. First, the relationship between the Young’s modulus and fracture density and orientation is analyzed. The Young’s modulus changes regularly with the variation of incident angles and azimuth, and the changing track is a cosine curve when the incident angle is fixed. The variation of the Young’s modulus increases with the increase of fracture density. Second, we use the Young’s modulus variation with azimuth to predict the fracture orientation. The Young’s modulus inversion algorithm for different azimuths of prestack seismic data and the ellipse fitting of the Young’s moduli in different azimuth with the least-squares algorithm are included in this proposed approach. Finally, we determine the advantage and robustness of our method in fracture-orientation estimation with synthetic and real-data examples. Compared with the conventional methods using AVO gradients, the direction of longer axis of the fitting ellipse of the Young’s modulus in different azimuth indicates the fracture orientation without ambiguity.