Fracture prediction is one of the challenges in exploration and development. This paper introduces a full-azimuth longitudinal-wave high-precision azimuthal gradient method, derives an amplitude response equation based on azimuthal impedance term coefficients and azimuthal anisotropy term coefficients that vary with the incident angle, and on this basis, derives a univariate quadratic amplitude response function with the sine square of the fixed azimuth incident angle as a variable. By differentiation, a linear change function of univariate amplitude gradient is obtained, proving that the amplitude gradient change in a fixed azimuth is linear, and the azimuthal anisotropic term coefficient is the main cause of the amplitude gradient change in a fixed azimuth, with its influence increasing as the incident angle increases. The larger the incident angle, the greater the anisotropic impact; it is proven that the amplitude change in a fixed azimuth has segmental partitioning, allowing for linear segmentation of the incident interval, calculating the amplitude gradient values of different segments, and then predicting pre-stack fractures by analyzing its azimuthal variation. The theoretical method has been implemented in software programming, developing new pre-stack fracture prediction software. The application in actual work areas has achieved good results, demonstrating that this method is accurate and reliable, capable of solving the prediction problems of formation micro-fractures, and can provide strong support for the exploration and development of complex fractured oil and gas fields.