In this work, a polarization-free coding metasurface is proposed to manipulate circularly polarized waves. Compared to a Pancharatnam-Berry phase metasurface, the proposed design not only allows for overcoming anti-symmetrical response characteristics between orthogonal circularly polarized states to enable achieving identical functionality under both right-handed and left-handed circularly polarized wave illuminations and avoiding polarization-conversion losses but also offers additional degree of freedom in the control of handedness. As a proof-of-concept demonstration, a polarization-free multi-bit coding metasurface is designed to realize helicity-switched holograms in the microwave region. Experimental measurements performed on a fabricated prototype reveal outstanding imaging quality with extremely high imaging efficiency above 76% for arbitrary polarizations at 10 GHz. Our proposed method expands the route in manipulating circularly polarized waves and can be applied over the whole electromagnetic spectrum for wavefront manipulation.