In this paper we propose the anti-reflection boundary design for planar graphene plasmons (GPs) circuits based on biomimetic moth-eye structures. The anti-reflection functionalities are investigated by analytical effective medium theory combined with transfer matrix method and numerical finite element method. Both analytical and numerical methods have shown that average reflection losses of 1% can be achieved within the mid-infrared region. Moreover, for plasmons with a very wide incident angle, the performance of such anti-reflection boundary could still be maintained, achieving less than 1% reflection up to 60? incident angle. The proposed moth-eye anti-reflection boundary would be helpful for the future development of high integration GPs circuits.