•3D modal parameters of a turbine blade are measured using a 3D CSLDV system.•Three laser spots continuously and synchronously move on a curved surface.•The extended demodulation method is used in CSLDV measurement on a curved surface.•Modal parameters from 3D CSLDV and SLDV systems have the same level of accuracy.•It takes the 3D CSLDV system 1/8 time to measure 1500 times more points. Modal parameters of a model turbine blade with a curved surface excited by white noise are identified by a novel general-purpose 3D continuously scanning laser Doppler vibrometer (CSLDV) system via an extended demodulation method (EDM). The proposed general-purpose system is calibrated to synchronously and continuously move three laser spots on the curved surface of the blade along the same scan trajectory and capture its 3D vibrations. The EDM is used to estimate its damped natural frequencies (DNFs) and 3D full-field undamped mode shapes. Identified modal parameters are compared with those from a commercial 3D scanning laser Doppler vibrometer (SLDV) system. Differences between their first six DNFs are less than 1.5%; their first six mode shapes are highly correlated as their modal assurance criterion values all exceed 95%. However, the 3D CSLDV system has much higher efficiency in obtaining 3D mode shapes of the blade than the 3D SLDV system.