Nitride perovskites are supposed to exhibit excellent properties as oxide analogues and may even have better performance in specific fields for their more covalent characters. However, till now, very limited nitride perovskites have been reported. In this work, a nitride perovskite LaMoN$_3$ has been systematically studied by first-principles calculations. The most interesting physical property is its ferroelectric $R3c$ phase, which can be stabilized under a moderate hydrostatic pressure ($sim1.5$ GPa) and probably remain meta-stable under the ambient condition. Its ferroelectric polarization is considerable large, $80.3$ $mu$C/cm$^2$, driven by the nominal $4d^0$ rule of Mo$^{6+}$, and the covalent hybridization between Mos $4d$ and Ns $2p$ orbitals is very strong. Our calculation not only predicts a new ferroelectric material with prominent properties, but also encourages more studies on pressure engineering of functional nitrides.