The electronic and thermal transport properties have been systematically investigated in monolayer C$_4$N$_3$H with first-principles calculations. The intrinsic thermal conductivity of monolayer C$_4$N$_3$H was calculated coupling with phonons Boltzmann transport equation. For monolayer C$_4$N$_3$H, the thermal conductivity (k{appa}) (175.74 and 157.90 W m-1K-1 with a and b-plane, respectively) is significantly lower than that of graphene (3500 Wm$^{-1}$K$^{-1}$) and C3N(380 Wm$^{-1}$K$^{-1}$). Moreover, it is more than the second time higher than C$_2$N (82.88 Wm$^{-1}$K$^{-1}$) at 300 K. Furthermore, the group velocities, relax time, anharmonicity, as well as the contribution from different phonon branches, were thoroughly discussed in detail. A comparison of the thermal transport characters among 2D structure for monolayer C$_4$N$_3$H, graphene, C$_2$N and C$_3$N has been discussed. This work highlights the essence of phonon transport in new monolayer material.
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