Searching for two-dimensional (2D) organic Dirac materials, which have more adaptable practical applications in comparing with inorganic ones, is of great significance and has been ongoing. However, only two kinds of these materials with low Fermi velocity have been discovered so far. Herein, we report the design of an organic monolayer with C$_4$N$_3$H stoichiometry which possesses fascinating structure and good stability in its free-standing state. More importantly, we demonstrate that this monolayer is a semimetal with anisotropic Dirac cones and very high Fermi velocity. This Fermi velocity is roughly one order of magnitude larger than that in 2D organic Dirac materials ever reported, and is comparable to that in graphene. The Dirac states in this monolayer arise from the extended $pi$-electron conjugation system formed by the overlapping 2emph{p}$_z$ orbitals of carbon and nitrogen atoms. Our finding opens a door for searching more 2D organic Dirac materials with high Fermi velocity.
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