A miniature single-grating nano-scal e displacement measuring system based on a 3×3coupler is developed.Based on t he laser Doppler effect and the scattering matrix theory of fiber couplers,a new symmetrical optical configuration is designed,and the nano-scale measurement precision is a chieved with the proposed phase demodulation algorithm.This method has the advantages of simple structure ,convenient adjustment, inhibition of air turbulence and insensitive to the waveleng th change,thus making the system have the merit of good robustness.Experiment results show that the Lissajou figures fo rmed by either two of the outputs of the 3×3coupler are smooth and clear,and their phase differences are reta ining around 120°,which illustrates that this method has excellent measurement stability.Numerical simu lation is well consistent with the theoretical analysis,and achieves a measurement precision of 8nm in the presenc e of both phase and amplitude errors,which proves the effectiveness of this meth od.