We investigate the thermodynamic properties of the potential superhard orthorhombic structure boron-carbonitride $\beta-BC_{2}N$ by using $ab$ $initio$ plane-wave pseudopotential density functional theory method within both local density approximation (LDA) and generalized gradient approximation (GGA). The lattice parameters ($a$, $b$ and $c$), equilibrium volume $V$, bulk modulus $B_{0}$ and its pressure derivative $B_{0}$' have been calculated, and compared with those of diamond and cubic boron nitride (c-BN). The obtained results are in excellent agreement with the available experimental data and other theoretical results. Through the quasi-harmonic Debye model, we also investigate the thermodynamic properties of $\beta-BC_{2}N.$ The variation of the thermal expansion $\alpha$, the heat capacity $C_{V}$ and the Grüneisen parameter $\gamma$ with pressure $P$ and temperature $T$, as well as the pressure-normalized volume ($P$-$V_{n}$) and the pressure- bulk modulus ($P$-$B$) relationship of $\beta-BC_{2}N$ are obtained systematically.