Recent years have seen vast progress in the generation and detection of vortex light, with potential applications in classical and quantum optics. However, it is still a challenge to efficiently generate high-fidelity vortex wavefronts in practical applications. Here, we propose a scheme to reconstruct the high-fidelity vortex wavefront via double dark resonances in a four-level atomic system. It is shown that, owing to a microwave field which interacts with magnetic or electric dipole moments of relevant atomic transitions, thereby generating spatially varying double dark resonances which in turn lead to the reconstruction of the incident probe field. In addition, to gauge the quality of the reconstructed probe field in comparison to the incident probe field, we study the fidelity of the reconstructed probe field and find that the reconstructed mode has a fidelity of more than 90% under the double-dark resonant condition. This study would be helpful to demonstrate optical vortex manipulation in atomic media.