A high-accuracy fluid refractive-index sensor based on an arrayed-waveguide grating (AWG) is designed. This system measures the refractive-index of a fluid in the groove using the characteristic of the sensibility of the phase shift of arrayed-waveguides. The phase shifts of the arrayed waveguides (AWs) lead to the position change of the maximum of the light intensity in the image plane of the output slab. The high accuracy real-time refractive-index of the fluid can be obtained from the power rate between two output waveguides via a narrow band source. A mathematical model based on the theory of Fourier optics and wave optics is established with reasonable parameters and the consideration of every factor. The analytic expression of the relationship between the refractive-index of the fluid and the power rate is obtained via fitting. The method can eliminate the instability, the inner loss of the instrument and the measurement error caused by the environment to improve the measurement accuracy of refractive index.