The characteristic of arrayed waveguide gratings is analyzed with the linear systems theory and the optical grating equation is educed. A new method for calculating the number of arrayed waveguide is proposed in consideration of reducing the crosstalk and gathering the radiating beam of light. This method is accurate and simple compared with the method given in Ref.[1]. The reason of causing the diffraction loss is analyzed, and the method to reduce the diffraction loss is introduced. As an example, 8×0.8 nm AWG multiplexer is designed with a center wavelength 1550 nm. The accuracy of this methods is proved by numeric model calculation.