A theoretical study of TE-wave propagation in a hollow circular waveguide with a graded dielectric medium is presented. The medium is modeled using a squared cosine function that oscillates between two unique complex dielectric media to simulate a periodic multilayer structure. The proposed model is applicable to arbitrary complex permittivities of the two media, including negative values for chiral metamaterials. The exact analytical result for the longitudinal magnetic field component H-z is obtained, while the transverse electric and magnetic field components could be determined using the appropriate Maxwell's equations.