We report continuously tunable and bandwidth variable optical notch and band-pass filters created by combining four left- and right-handed circular cholesteric liquid crystal cells without extra optical components. Filter performance was greatly improved by introducing an anti-reflection layer on the filter device. The filter comprised cholesteric liquid crystal wedge cells with continuous pitch gradient. The band wavelength position was spatially tuned from 470 nm to 1000 nm. The notch filters are polarization-independent in the spectral ranges. The band pass filters can be designed to be polarization-independent or polarization-dependent via cell alignment and the bandwidth can be reversibly controlled from the original bandwidth (60~18 nm). These tunable filter strategies could make a paved road to wavelength tunable spectroscopic instruments applications in the VIS and near infrared response spectral range.