Intensity saturation is a challenging problem in structured light 3D shape measurement. Most of the existing methods achieve high dynamic range (HDR) measurement by sacrificing measurement speed, making them limited in high-speed dynamic applications. This Letter proposes a generic efficient saturation-induced phase error correction method for HDR measurement without increasing any fringe patterns. We first theoretically analyze the saturated signal model and deduce the periodic characteristic of saturation-induced phase error. Based on this, we specially design a saturation-induced phase error correction method by joint Fourier analysis and Hilbert transform. Furthermore, the relationship among phase error, saturation degree, and number of phase-shifting steps is established by numerical simulation. Since the proposed method requires no extra captured images or complicated intensity calibration, it is extremely convenient in implementation and is applicable to performing high-speed 3D shape measurements. Simulations and experiments verify the feasibility of the proposed method.