Advanced three-dimensional (3D) imaging techniques can acquire high-resolution 3D biomedical and biological data, but available digital display methods show this data in restricted two dimensions. 3D light-field displays optically reconstruct realistic 3D image by carefully tailoring light fields, and a natural and comfortable 3D sense of real objects or scenes is expected. An interactive floating full-parallax 3D light-field display with all depth cues is demonstrated with 3D biomedical and biological data, which are capable of achieving high efficiency and high image quality. A compound lens-array with two pieces of lens in each lens unit is designed and fabricated to suppress the aberrations and increase the viewing angle. The optimally designed holographic functional screen is used to recompose the light distribution from the lens-array. The imaging distortion can be decreased to less than 1.9% from more than 20%. The real time interactive floating full-parallax 3D light-field image with the clear displayed depth of 30 cm can be perceived with the right geometric occlusion and smooth parallax in the viewing angle of 45°, where 9216 viewpoints are used.