The spectral response of a chirped sinusoidal surface relief grating in an optical waveguide has been studied by means of Local Normal Mode Expansion theory. A matrix technique has been applied to account for the varying grating period. The grating is divided into segments with constant periods and coupling coefficients. Nonslanted grating is considered in a first-order diffraction. Also, contradirectional coupling between guided modes in phase synchronism at an arbitrary angle of incidence is considered. Performance considerations include TE-TE, TE- TM, and TM-TM mode coupling for different grating geometry and waveguide parameters. We show the effect of geometry and waveguide parameters on the performance of the chirped grating as a wavelength demultiplexer. Also, we demonstrate how the filtering and demultiplexing characteristics and the spectral shift between different polarization modes can be controlled.