Two novel two-dimensional (2D) carbon allotropes named C_y and C_z with large meshes are predicted based on first-principles calculations. Their formation energies are lower than that of graphdiyne, which was recently synthesized in an experiment. Molecular dynamics simulations indicate that C_y and C_z are stable even when the temperature is over 1000 K. The calculated Poisson's ratios of C_y and C_z show their anisotropic mechanical properties. The electronic structure calculations indicate that C_y is a metal, while C_z behaves as a semiconductor. Moreover, C_z shows conductive anisotropy suggesting its potential in nanoelectronic devices. Meanwhile, their well-defined mesh structures are suitable for molecular sieves.