This work proposes a new global FD-RTM method to solve the problem of ultrasonic inspection of parts with complex geometric shapes. With this method, the frequency domain reverse time migration (FD-RTM) algorithm is used to adapt to the complex refraction of ultrasonic waves by the surface, while an interface solution algorithm based on tangent fitting is used to solve the interface position with high precision through the full matrix reception data. Based on high-precision interface information, a hybrid extrapolation algorithm and a situation-specific probe movement strategy are used to enable the probe to find the next sampling point according to the direction of the workpiece surface, allowing complex surface topography features to be identified without relying on the workpiece CAD drawing. This makes it possible to achieve the automated inspection of workpieces. To verify the proposed method’s effectiveness, an aluminum alloy model with side-drilled holes (SDH) is used. The geometry of the model consists of multiple convex and concave surfaces. By comparing the local FD-RTM imaging with images synthesized using the entire scan path, it is shown that gFD-RTM improved the imaging performance. Compared with FD-RTM, the average signal-to-noise ratio of gFD-RTM was increased by 20%, and the array performance index (API) was reduced by 70%, indicating effective detection coverage.