Liquid crystal tunable filters (LCTF) are extensively used in hyperspectral imaging systems to successively acquire different spectral components of scenes by adjusting the center wavelength of the filter. However, the spectral and spatial resolutions of the imager are limited by the bandwidth of LCTF, and the pitch dimension of the detector, respectively. This paper applies compressive sensing principles to improve both of the spatial and spectral resolutions of the LCTF-based hyperspectral imaging system. An accurate transmission model of the LCTF is used to represent its bandpass filtering effects on the spectra. In addition, a random coded aperture placed behind the LCTF is used to modulate the spectral images in the spatial domain. Then, the three-dimensional encoded spectral images are projected onto a two-dimensional detector. Benefiting from the spectral-dependent transmission property of the LCTF, information of the entire spectrum is collected by a few snapshots using different center wavelengths of the LCTF. Super-resolution hyperspectral images can be reconstructed from a small set of compressive measurements by solving a convex optimization problem. Simulations and experiments show that the proposed method can effectively improve the spectral and spatial resolutions of traditional LCTF-based spectral imager without changing the structures of the LCTF and detector. Finally, a multi-channel spectral coding method is proposed to further increase the compression capacity of the system.