In this work, the effect of the acrylonitrile content on the structure and dynamic behavior of nitrile rubber is systematically studied during the glass transition process by employing all atom molecular dynamics simulation. For the static property, the polymer density and the energy are calculated. The polymer density, the non-bond energy and the torsional energy are found to play an important role during the glass transition process. For the dynamic property, the translational mobility, the bond reorientation mobility, and the dynamic heterogeneity on the chain backbone are analyzed. The mobility on the chain backbone declines with improving the acrylonitrile content. Meanwhile, the glass transition temperature (Tg) obtained from the non-bond energy and the torsional energy is larger than that from the polymer density. Furthermore, the Tg obtained from the dynamic heterogeneity is largest compared to those from the bond reorientation mobility or the atom translational mobility. Especially, according to the mean-square fluctuations of the backbone atoms, the immobile atoms are distinguished. Then, the percolation probability of the immobile domain is analyzed by characterizing the size of the largest immobile domain and the number of the immobile domains. By observing the snapshots of the mean-square fluctuations of atoms, the percolation transition of the immobile domains is clearly observed, which can help to understand the glass transition process for different acrylonitrile contents.