Engineering materials with high thermal conductivity are of fundamental interest for efficiently dissipating heat in micro/nanoelectronics. Using first principles computations we report an ultra-high thermal conductivity of 2090 Wm⁻¹K⁻¹ (1395 Wm⁻¹K⁻¹) for hexagonal pure (natural) BC₆N(h-BC₆N). This value is among the highest thermal conductivities known after diamond and cubic boron arsenide. This ultra-high lattice thermal conductivity (k) is mainly attributed with high phonon group velocities of both acoustic and optical phonons arising from strong Csingle bondC and Bsingle bondN bonds as well as the light atomic mass of the constituent elements such as boron (B), carbon (C) and nitrogen (N). We also report size dependent thermal conductivity of h-BC₆N nanostructures by including boundary scattering. At room temperature (300 K) and at nanoscale length (L) of 100 nm, a high k value of 175 Wm⁻¹K⁻¹ is observed (higher than the bulk k value of silicon). Optical phonons with large group velocities are mainly responsible for this high thermal conductivity in h-BC₆N nanostructures. High thermal conductivity of h-BC₆N makes it a candidate material for heat dissipation in micro/nano thermal management applications.