Key components with complex curved geometries are widely found in various industrial structures, where internal defect detection faces significant challenges due to acoustic beam distortion and unstable coupling conditions. To address this issue, a flexible ultrasonic array and an adaptive imaging method for the inspection of complex curved components are proposed. A flexible ultrasonic array capable of conformal attachment to irregular surfaces is designed and fabricated. Considering that geometric deformation induced by conformal attachment of the flexible array introduces spatial position deviations of array elements, which consequently lead to inaccuracies in propagation delay calculations in total focusing method (TFM) imaging, an adaptive TFM imaging approach based on known boundary features is developed. The proposed method does not rely on external positioning devices. Instead, geometric boundaries such as the bottom surface of the inspected component are used as internal references. Relative time delays between array elements are estimated using normalized cross-correlation, enabling reconstruction of the actual array geometry and adaptive correction of the delay law in TFM imaging. As a result, phase mismatches caused by conformal attachment of the flexible array are effectively compensated. Numerical simulations and experimental validations are conducted to comparatively analyze TFM imaging performance before and after adaptive calibration. For curved specimens with an overall inspection scale on the order of hundreds of millimeters, the minimum localization errors of internal artificial defects after adaptive calibration are 2.16 mm in the lateral direction and 1.48 mm in the axial direction, respectively, allowing stable and clear reconstruction of defect positions. Meanwhile, geometric imaging artifacts are effectively suppressed, and the overall signal-to-noise ratio is significantly improved. The results demonstrate that the proposed flexible ultrasonic array combined with the adaptive imaging method enables reliable high-accuracy defect localization under complex curved surface conditions, providing an effective approach for ultrasonic nondestructive testing of complex curved components.