A novel arrayed-waveguide grating (AWG) based on unbent waveguides is analyzed. The arrayed waveguides are replaced by unbent waveguides and two graded-index planar waveguides (GISLAB) are used as input and output planar waveguides,respectively. This design can decrease the size of the coarse wavelength division multiplexing (CWDM) effectively. A mathematical model of the AWG is established based on the theory of Fourier optics and wave optics,with reasonable parameters considering every factor. The novel arrayed waveguide grating with asymmetric focal lengths of GISLABs is discussed,whose background noise is degraded by 20 dB with respect to the symmetrical structure,and which will widen spectral width. The method of reducing the size further with a reflector and the property of the routing is designed.