  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 2\emph{p}$_z$ orbitals of carbon and nitrogen atoms. Our
finding opens a door for searching more 2D organic Dirac materials with high
Fermi velocity.
