Designing new materials with reduced dimensionality and distinguished properties has continuously attracted intense interest for materials innovation. Here we report a novel two-dimensional (2D) Zn2C monolayer nanomaterial with exceptional structure and properties by means of first-principles calculations. This new Zn2C monolayer is composed of quasi-tetrahedral tetracoordinate carbon and quasi-linear bicoordinate zinc, featuring a peculiar zigzag-shaped buckling configuration. The unique coordinate topology endows this natural 2D semiconducting monolayer with strongly strain tunable band gap and unusual negative Poisson ratios. The monolayer has good dynamic and thermal stabilities and is also the lowest-energy structure of 2D space indicated by the particle-swarm optimization (PSO) method, implying its synthetic feasibility. With these intriguing properties the material may find applications in nanoelectronics and micromechanics.