Fracture systems in nature are complicated. Normally vertical fractures develop in an isotropic background. However, the presence of horizontal fine layering or horizontal fractures in reservoirs makes the vertical fractures develop in a VTI (a transversely isotropic media with a vertical symmetry axis) background. In this case, reservoirs can be described better by using an orthorhombic medium instead of a traditional HTI (a transversely isotropic media with a horizontal symmetry axis) medium. In this paper, we focus on the fracture prediction study within an orthorhombic medium for oil-bearing reservoirs. Firstly, we simplify the reflection coefficient approximation in an orthorhombic medium. Secondly, the impact of horizontal fracturing on the reflection coefficient approximation is analyzed theoretically. Then based on that approximation, we compare and analyze the relative impact of vertical fracturing, horizontal fracturing and fluid indicative factor on traditional ellipse fitting results and the scaled B attributes. We find that scaled B attributes are more sensitive to vertical fractures, so scaled B attributes are proposed to predict vertical fractures. Finally, a test is developed to predict the fracture development intensity of an oil-bearing reservoir. The fracture development observed in cores is used to validate the study method. The findings of both theoretical analyses and practical application reveal that compared with traditional methods, this new approach has improved the prediction of fracture development intensity in oil-bearing reservoirs.