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A broadband electrically tunable variable polarizer for fiber systems based on a liquid crystal lens is proposed and demonstrated. The polarization selectivity is based on a polarization-sensitive coupling efficiency to the fiber in the fiber system. For an incident ordinary ray, the output beam size remains the same as that of the incident beam, which results in low coupling efficiency. For an incident extraordinary ray (e-ray), the output beam size is close to the size of the fiber core, giving rise to high coupling efficiency because of the lens effect. Moreover, the output beam size of the e-ray can be electrically controlled, thus allowing the optical attenuation to be manipulated. In our experiments, the polarization-dependent loss from the visible to the near-infrared spectral region was approximately 12 dB. Such a broadband electrically variable polarizer may be applied to various designs for fiber-optic sensing devices and polarization-sensitive optical instruments.