Phase unwrapping is a key problem of phase-shifting profilometry vision measurement for complex object surface shapes. The simple path-following phase unwrapping algorithm is fast but has serious unwrapping error for complex shapes. The Goldstein+flood phase unwrapping algorithm can handle some complex shape object measurement; however, it is time consuming. We propose a fast phase unwrapping algorithm based on region partition according to a quality map of wrapped phase. In this algorithm, wrapped phase image is divided into several regions using partition thresholds, which are determined according to histogram of quality value. Each region is unwrapped by using a simple path-following phase algorithm and several groups with different priorities are generated. These groups are merged according to their priorities from high to low order and a final absolute phase is obtained. The proposed method is applied to wrapped phase images of three objects with and without noise. Experiments show that the proposed method is much faster, more accurate, and robust to noise than the Goldstein+flood algorithm in unwrapping complex phase image.