Heat removal has become a significant challenge in the miniaturization of electronic devices, especially in power electronics, so semiconducting materials with suitable band gaps and high lattice thermal conductivity are highly desired. Here, through first-principles calculations, we theoretically predict an ultra-high and anisotropic lattice thermal conductivity in monolayer BC2N. The predicted values of lattice thermal conductivity at room-temperature are 893.90 W m−1 K−1 and 1275.79 W m−1 K−1 along the armchair and zigzag directions, respectively. These values are probably the highest that have ever been reported for two-dimensional semiconducting materials. Such high lattice thermal conductivities are attributed to the high vibrational frequencies, large phonon group velocities, long phonon lifetime, low phonon anharmonicity, and strong bonding in monolayer BC2N. We also calculate the electrical and electronic thermal conductivities, which are also very high. Based on these theoretical findings, we expect monolayer BC2N to be an adequate candidate for thermal management in nanoelectronic devices.