Abstract: Mechanical metamaterials with negative Poisson′s ratio have been widely application in the aerospace, armarium, national defence construction and other fields owing to its outstanding mechanical properties. This paper proposes an arc angle changeable circular curve honeycomb core. It optimized the traditional re-entrant auxetic cellular structures. We adopted energy method to figure out the theory formulas of effective elastics modulus and Poisson′s ratio in every feasible arc angle, results of theory formulas and results of finite element simulations are of quite consistent so it approves the correction of the theory formulas. Meanwhile, the effects of the arc angle, the length−width ratio of honeycomb core elements and the thickness of the rod on effective elastic modulus and Poisson′s ratio are investigated. This paper may fulfill the great potential of mechanical metamaterials with negative Poisson′s ratio.