Diffractive optical elements suffer from large chromatic aberration due to the strong wavelength-dependent nature in diffraction phenomena, and therefore, diffractive elements can work only at a single designed wavelength, which significantly limits the applications of diffractive elements in imaging. Here, we report on a demonstration of a wavefront coded broadband achromatic imaging with diffractive photon sieves. The broadband diffraction imaging is implemented with a wavefront coded pinhole pattern that generates equal focusing power for a wide range of operating wavelength in a single thin-film element without complicated auxiliary optical system. Experimental validation was performed using an UV-lithography fabricated wavefront coded photon sieves. Results show that the working bandwidth of the wavefront coded photon sieves reaches 28 nm compared with 0.32 nm of the conventional one. Further demonstration of the achromatic imaging with a bandwidth of 300 nm is also performed with a wavefront coded photon sieves integrated with a refractive element.