Molecular dynamic simulations are carried out to study the static and dynamic properties of topological polymer brushes by taking into account chain stiffness and their topological feature. It is found that chain stiffness plays an important role in topological polymer brushes, and there exists scaling laws for the radius of gyration against chain stiffness and topological feature, indicating that bending interaction is as important as topological constraint. An empirical finitely extensible nonlinear elastic force in terms of chain stiffness and topological features is also obtained by fitting related parameters. A simulation on the invasion of free polymer chains from environment into a ring polymer brush shows that under pressure, such kind of penetration depends largely on chain stiffness, in contrast to the minor influence of topological structure, which seems to be suppressed