Starting from the conventional coupled-mode theory and using the mode transformation method, a unified local mode approach is presented to analyze the chiral fiber long-period gratings (CLPGs) formed by twisting a high-birefringence fiber as an example of a chiral fiber with double-helix symmetry. Similarly, a helical-core fiber, as an example of single-helix CLPGs, is analyzed by using the ideal mode approach. The coupled-mode equations for both the cases are transformed and reduced to two-mode equations. The derivation is simple, and the results are explicit in concept. These results reveal the scheme of polarization selectivity of mode coupling, and for the first time, the necessary condition for achieving the polarization selection is given. The analysis indicates that conventional coupled-mode theory is efficient for studying chiral fiber grating, and more importantly, it is better to be understood. A numerical simulation has been done on a twisted conventional Panda fiber with a beat length of 2.5 mm. It has been shown that in a right-handed twisted structure, a total power transfer of a right-handed circular polarization light is obtained with a grating pitch of 0.382 mm and a grating length of 64.9 mm at the wavelength of 1.55 μm . On the other hand, through the simulation on single-helix CLPG with an eccentric core, it has been shown that a total power transfer of the core mode to LP11 mode is obtained with a grating pitch of 0.723 mm and a grating length of 10.46 mm at the wavelength of 1.55 μm.