Molecular dynamics simulations have been performed to study the effects of the cross-link density and distribution on the network topology, the dynamic structural properties, the tensile mechanical properties, and the viscoelastic properties of chemically cross-linked polymers. Simulation results show that the introduction of cross-links slows the chain dynamics down and thus leads to a slight increase in the glass transition temperature. Improving the cross-link dispersion state is found to be essentially equivalent to increasing the effective cross-link density, as reflected in the network topological features. The structural relaxation behavior is analyzed in terms of the incoherent intermediate dynamic structure factor, and the characteristic a-relaxation time is examined by the MCT and VFT equation. The results indicate that the time temperature superposition principle holds on the segmental length scale but fails on the chain length scale, where it can be valid at sufficiently high temperature above the critical temperature. Furthermore, the mechanical property of polymer networks is slightly influenced by the introduction of cross-links at small length scales but is significantly improved at large length scales. The polymers with high cross-link density or uniform cross-link distribution exhibit an upturn in the modulus at large deformations in Mooney-Rivlin plots due to the finite chain extensibility. By accounting for the topological defects and the cross-link constraint, the phantom model is shown to predict the network behavior well within relatively large deformations. The viscoelastic properties of polymers such as the storage modulus, the loss modulus, and the loss tangent show a positive exponential relation with the apparent cross-link density. This work may shed some light on the relevant experimental and theoretical studies on cross-linked polymers.