A simulation method is proposed to study the amorphous structure of carbon nitride. The material properties of a non-uniform nitrogen distribution in an amorphous CN matrix can be studied. The cohesive energy of a group of randomly generated atoms can be minimized to find the relative positions of atoms. From the calculated configuration of atoms, many properties of amorphous carbon nitride can be calculated such as bulk modulus, P-V curve, sp$^3$/sp$^2$ ratio of carbon, and vibrational spectra. The calculation shows that the cohesive energy of non-uniform nitrogen distribution is lower than that of a uniform distribution. This may suggest that the regular structure of carbon nitride can at most be metastable. It is not easy to incorporate nitrogen atoms into a carbon matrix.