the chiral fiber long-period gratings (clpgs) could be fabricated by twisting a high-birefringence (hi-bi) fiber. however, when it is immersed into a material whose refractive index (ri) is higher than that of the cladding, there exists a complicated coupling between the core modes and the radiation ones. in this paper, for the first time to our knowledge, we theoretically investigate the mode coupling characteristics in such a clpg. it is found that, owing to a strong mode transfer from the co-handed core mode to continuous radiation ones under the phase-matching condition, the clpg can be regarded as a broadband circular polarizer since only the cross handed circularly polarized light is left when a linearly polarized light is injected. furthermore, the influence of the ri of the surrounding medium on the bandwidth and extinction ratio of this circular polarizer is investigated in detail. as a result, a broadband all-fiber circular polarizer can be constructed. considering its simple configuration, it might have some potential applications, such as filters, broadband polarizers, and sensors.