Based on the analysis solution of a W-type double-cladding chiral optical fiber, the optical power characteristics of several lower-order guided modes have been investigated. The optical power in the core as a function of chirality parameters in the core, the inner and outer claddings is calculated for different inner cladding thickness. The effect of chirality parameters on the optical power in the core for guided modes with different index signs is discussed. Thicker inner cladding results in larger optical power in the core. With increasing the chirality parameter in the core, the optical power of HE-11 mode and HE-21 mode (HE01 mode) in the core increase slowly, but the power of HE11 mode and HE21 mode (HE02 mode) in the core decrease gradually. The effect of the chirality parameter in the cladding is reversed with that in the core.