In this paper, a high-performance 5G radome based on absorptive meta-surface is proposed, where an unit cell structure consists of a dielectric layer which is sandwiched between a top lossy layer and a bottom metallic layer. The thickness of radome is designed only 0.037λ, where the simulation results show that the proposed radome is totally transparent to the working band from 3.2 GHz to 3.8 GHz, with an insertion loss less than 0.2dB. Moreover, the spurious signals from 6.5GHz to 7.5GHz could be highly absorbed, with the absorption efficiency more than 90%. The radome is independent to the electromagnetic(EM) waves in both TE and TM modes. The working principle of this radome is also explained reasonably in the perspective of the equivalent circuit model. These results are quite helpful in designing the miniaturized antenna device for 5G communications, radar and military communications.